That’s one definition, but more generally a “catwalk” is a narrow walkway such as above a stage, through a tunnel , next to a bridge - and also the sort of narrow platform a model walks on that extends out into the audience. So I can see how “narrow walkway” gets used for buildings with exterior hallways.
Plus one for “garden apartments.” In my New England dialog, this would apply regardless of whether all the apartments are on the ground floor or below grade, as some have suggested. Looking for definitions online supports some of the alternatives definitions here. Like “original miles,” “garden apartment” clearly means something to the user, which is absolutely unknowable to the listener.
Everywhere I have lived (Md., Mich., D.C., Va.), “garden apartments” are three-story buildings with maybe 12-18 units per building with some green space, and all the units having entrances to the outside. I lived in a condo like this on the third floor and my door opened to the outside, which in this case was a covered outdoor hall.
I first heard this term when I moved to D.C. in 1983. Never heard it anywhere else.
To me “a” garden apartment is the ground or somewhat below ground unit of a building that has multiple floors of which the garden level is not the “main” floor. This could be a basement level apartment in an otherwise single-family home, or a sizable multi-unit building.
That said, “garden apartment” when applied to the whole building usually means suburban apartments in a park-like setting with parking in front and small lawn plots in back that can be used by each individual unit. They may be multi-story but usually they’re multi-story units rather than the units being separated by floor, though there’s always variants.
I’ve not seen anyone mention the term “walk-up” yet. That’s pretty common in Chicago (as is the first “a” garden apartment usage). These are usually multi-unit buildings with access provided by one or more stairwells rather than central hallways. There can be ground floor units directly accessible from outside or from the entry vestibule. They were more common in the pre-WWII era and fell out of favor because it’s usually impossible to install elevators, and height is limited to about four or five stories. Plus stairs are expensive. The 34-unit apartment I live in was built in 1915 and it has eight stairwells (four front stairs and four rear stairs). Each stair only serves eight apartments spread over four floors. There’s also two basement apartments which could conceivably be called the garden level. 
I’ve only heard the term “walk-up” used to refer to apartment buildings without elevators. Nothing to do with how many stairwells or how to access them or hallways, just that there are no elevators to higher floors. This is in NYC. When I first moved here I lived on the 6th floor of a 7 story walk-up.
Townhouse?
Same here - I suspect that the usage in Chicago is similar and the building @jjakucyk is a special case. I also wonder if he’s talking about something like this - there is no elevator , as there are only three floors. Each entrance and stairwell leads to six apartments ( two on each floor) and they are part of the same complex rather than having separate ownership - but they are actually separate buildings each with six apartments.
Can’t be a townhouse if it’s not in a town
Some suburban garden apartments do use that term, though more often they’re condos. My admittedly pedantic take is that to truly be a townhouse it has to front a public street and have fee simple ownership. If it faces a parking lot and is part of a private development then the townhouse term is just real estate agent dressing.
While technically walk up can apply to any building without an elevator, my perception is that it generally refers to those that don’t have internal hallways and the only interior public space is the stairwells. Not saying that’s a hard and fast rule, but I think it better exemplifies the term itself. It seems like most courtyard apartments from the 1910s and 1920s are also walk ups.
The only thing a walk-up apartment means is that there is no elevator. Hence the “walking up” aspect. I’m not sure why you think hallways have any relevance.
Where I live the term “own door apartment” is used.
Because generally buildings called walk ups are tall/narrow and only have stairs not halls. Walk up, not walk along. I didn’t say they can’t have halls, but usually elevator-less buildings with significant internal hallways are just called apartment buildings, not walk ups, because you don’t walk up to your particular unit. Again, not saying this is sacred, but that’s been my experience.
They do have halls. They are short halls and if there are only two apartments per floor, it might be more of a “lobby” than a hall in shape - but no hall at all would mean you walked up the stairs and were directly at the apartment door or went through the apartment door and walked up the stairs ( which are inside the apartment) That doesn’t happen in a building with more than two units.
And “walk-up” refers to walking up to the third or fourth floor rather than taking an elevator,
Er, what? How else would you get up to your floor if there is no elevator without walking up the stairs? Use an outside pulley system like in Amsterdam?
And like @doreen said, they do have halls. I’m not sure how you could have more than two apartments per floor without some type of hallway between them.
Stairs have landings when you change direction, that’s where the doors are. For example, you walk in the front door of the building, then there’s a door on your right and a door on your left to each of the two first floor units. Then you walk up half a flight of stairs, turn 180-degrees at a landing, then walk up another half a flight, then you get to the landing at the top where there’s two doors at either side to the second floor units, in this case for a four-unit building. The intermediate landing has no doors. There’s no hall either. Halls are separate from stairs, especially when talking about fire code. There should always be a door between the stairwell and any hallway in a multi-unit building.
I’ve lived in buildings with entrances on two different levels because of the slope of the terrain around it. Other buildings in the same complex would have entrances at either end directly into the stairwell at the half-floor level, where you could walk up half a flight to the first floor or down half a flight to the basement. The difference there is that once your reached your floor, you went through a door to a long hallway that went from one end of the building to the other, and all the units were accessed from there. No units had access directly into the stair.
I think part of the disconnect is that in your view there should always be a doorway between a hallway and a stairwell and therefore you are defining some things I would call a “hall” as a “landing” .
I’m going to describe a building style I know well. You walk up some steps from the sidewalk and enter the front door. Sometimes there’s a vestibule and then you go through another door. You walk past the two front apartments and then there is a stairway where you go up a couple of steps, turn and go up a couple of more and turn again, and are now facing 180 degrees from where you entered the staircase. When you get to the second floor, there are two apartments (the rear) to your left and two to your right ( the front) with of course a hall connecting them.
Another style with two apartments on each floor has you entering a house. The stairway is to the right and a hallway is on the left . The hallway ends at two apartment doors. The stairway goes up to the second floor - if you continue walking straight, you will end up at the apartment doors. To get to the third floor, you walk down a hallway that runs outside one of the apartments… I just managed to find a photo of what I’m talking about - this is a building with two apartments on each floor. ( Each apartment has two doors , one at the front and one at the rear) When you get to the top of the stairs , you will turn left and go down a hallway to get to a stairway directly over the one pictured.
In St. Louis, it’s an old-fashioned regionalism to call a dwelling in a multi-family building with its own door to the outside a “flat” and a dwelling which opens into a hallway or common entrance as an “apartment.” By this usage, flats are what’s referred to in other places as duplexes/triplexes/fourplexes. I’ve never heard this used anywhere else, and the usage is fading as the older generations die off.
In Britain and Ireland there is a distinction made between flats and apartments but it’s not on the basis of whether the door opens to outside. Flats and apartments are pretty much the same thing except apartments are more “posh”. An apartment building made up of “flats” (as opposed to apartments) is called a “block of flats”.
My immediate thought was that it has to be cheaper for the owner not to have interior spaces requiring air conditioning. But then two questions came immediately to mind: (a) Is there any law that would require the landlord to climate-control the corridors? and (b) What is the difference in expense between AC-ing the halls in a hot location like Arizona versus heating them during a winter in, say, Fargo? If the cost of AC is meaningfully greater, this could serve as incentive to minimize or eliminate interior corridors in hot climates that is comparatively reduced in temperate or colder areas.
That’s what it means to me. And, no, I wouldn’t call an apartment above ground level as a garden apartment, though a below grade apartment could be one.
Having lived in Phoenix & Las Vegas for ~20 years …
An un-airconditioned interior corridor would be an immediate sign you’re renting in what’s effectively a tenement. Not going to happen in any apartment complex that is aiming at any higher rental rate or higher SES customer.
As to cost, AC in the desert and heat in the frozen North are pretty similar on a cost per month per square foot basis. AC might be slightly less than heat, but only slightly.
But for any given apartment owner/designer, that’s not the comparison that matters. The comparison they care about is: “Which is cheaper: Cost of AC for hallways versus cost of no AC with no hallways?” That’s always an easy decision.