I’m sure you mean that it isn’t numbered 13,unless your building just has a gaping hole between 12 and 14…
Balthisar, a one storey building is called just that, or more commonly a “single storey building”.
The first floor is the second storey, yes. The two terms are used in slightly different ways, so there is not much confusion. For example, your “Excuse me, where is the menswear department?” wouldn’t be answered with “on the second storey”, but I assume it wouldn’t be in the US either. “Storey” is only used when talking about the actual building itself, and not its contents or tenants.
I can only recall one building I’ve seen that has more than one labeled underground floor, and in that case they were labeled “B” (basement) and “SB” (sub-basement). I expect multiple underground floors would be labeled something like B1, B2, etc, with B1 being closest to ground level. This particular building (in the US) also happened to have a ground floor and a first floor, with the ground floor being solely a large lobby area. Quite a few people would, when going down in the elevator, get off on first floor and look around puzzledly, wondering why this didn’t look like it did when they entered the building.
I think I’d be inclined to answer someone in this manner: “Oh, mens’ wear? That’s up on the second story.” Or equally I’d say “…second floor,” or even “…second level,” in my American sense all three being the same. Maybe that’s why we Americans do it differently.
In most buildings I’ve been in where a below ground floor is actually used it is simply referred to as basement, or ‘B’ in the elevator. If there are two floors below ground, they are labeled ‘B1’ and ‘B2’. However when I got to Vanderbilt University, I found that in the Stephenson Science Center there are five floors, two below ground and three above. But they simply label them as floors 1 through 5, so you enter the building on the ‘third’ floor, and the ‘first’ and ‘second’ floors are below ground.
Our local hospital (UK) is the same, except make that 11 floors. You enter the building on the third “level”, which is the “3” button in the lift. Level 2 is for laundry / catering / offices etc. People regularly, on their way out, hit “1” for the lobby and find themselves in the bowels of the building - reserved for Og knows what horrors. Such people usually arrive back up on level 3 looking shaken. 
The same system is used in Panama, and AFAIK in the rest of Latin America. The ground floor is called the planta baja, abbreviated “PB” on elevators. The next one up is the “first floor,” primer piso.
The building where I work is built on a hillside. The main front entry is two floors above the rear entry from the parking lot. The main entry is called the planta baja, while the levels below it are the sotano (basement) and subsotano (sub-basement). But the office numbering system starts on the 100 level in the sub-basement.
It’s the only building I know of that has an index posted in the elevator:
4th Floor = 700 level
3nd Floor = 600 level
2nd Floor = 500 level
1st Floor = 400 level
PB = 300 level
S = 200 level
SS = 100 level
In New York City commercial buildings, below-ground levels are usually referred to as concourse levels. The first level below ground is usually referred to as Concourse A or 1, the second Concourse B or 2 and so forth.
Not in the building where I work, a corporate headquarters. I can think of several other office buildings in my city that have a ground floor, above which is the first floor.
The university I attend uses the European system for this. Ground floor, then first on the level above. Rooms on the ground level are numbered with only two digits. In other words, room 25 is on the ground level, above that is room 125 on the second floor, and so on. It’s caught me off-guard a few times and I don’t think I’ve seen it used anywhere else in the U.S.
I had an amusing anecdote to post here.
But that’s another story.
I stayed in a house in Tyrrol which sort of explained it to me. In this house, and in most of the houses in the town, the street-level part of the building… the ground floor, I guess… was divided into commercial space and an entrance for people who lived in the apartments above. So, the people who actually lived in the building got to live in the first, second, third, fourth, and fifth (that was me–garret apartment) floors; the shop that occupied the commercial space was simply… well, at the street address. Actually, the first and second floors were joined into a very large apartment, occupied by the people who owned the whole house.
The American university I attend has mostly split-level buildings. The level that is half buried is called the Ground floor, and is numbered with the letter G plus two digits. The floor above it is the Main floor, with rooms in the 100s; then second floor in 200s, and so on up. If there is anything below the ground floor, it is called B1, B2, etc (for basement, of course), and the rooms are labeled with B plus the appropriate three digits.
I disagree. Buildings that skip numbering a 13th floor are rare in the U.S. Most buildings taller than 12 floors do have a floor numbered 13.
Let’s look at the tallest buildings in the United States:
- Sears Tower, Chicago. Yes — the 13th floor’s ZIP+4 is 60606-6412. Ernst & Young is on the 13th floor.
- Empire State Building, New York. Yes.
- AON Center (formerly Amoco Bldg.), Chicago. Yes — the 13th floor’s ZIP+4 is 60601-6424.
- John Hancock Center, Chicago. Yes — HLB Communications is on the 13th floor.
- Chrysler Building, New York. No floor numbered 13.
Maybe this should be divided into office buildings and others. Almost every hotel in the US that I have stayed in with more than 13 floors has the number 13 omitted from the elevator buttons and room keys. This might be because people who work in a building every day (and besides - who is going to complain about your office being on the 13th floor?) are less suspicious of the building itself. With a hotel, how many people would refuse to stay in a 13th floor room for one night?
I have no idea, but it’s obviously enough for hotels to remove that floor from their database.
Once again I have no contribution to the OP, but just anecdotal evidence to support a tangential observation. 
In Hong Kong, the Chinese use U.S. style and the English use english style, and if you speed both languages thats confusing!!!
I work in a hotel and we have no room 13 on any floor!!!
Spelling and grammer subject to change with out notice.
There is no floor zero.
That’s why the millenium started in 2001.
I mean, duh.
I’ve noticed here in NY that the thirteen-skipping phenomenon is pretty common in commercial buildings, but hardly universal - in my own experience, two of the three buildings I’ve worked in followed it. I wonder if the reason my current office building has a 13th floor is that it’s the oldest by at least a decade - I’d estimate it was built in the teens, where the other two were built in the late 20s and the early 50s, respectively.
For residential buildings, I have less of a data base - few of my friends live in high-rises. But I’ve heard from real-estate folks that people really don’t want to live on the 13th floor, even if they can stand on to work on it. My one friend who does live in a high-rise lives in Apartment 14A - of course, it’s on what ought to be the thirteenth floor. (FWIW, the building’s from 1962.)
Oh, and as for “a gaping hole,” you can achieve much the same effect by cramming mechanical systems on the true 13th floor. The first building I worked in did that.
To make matters even more confusing, the buildings here almost always use the North American system, but with French nomenclature (rez-de-chaussée, deuxième étage…)
The ones I can’t stand are when you go into an elevator and are confronted with about five different floors (Lobby, Concourse, Atrium, Mezzanine, and Grand Hall or something) with no indication as to which one contains the entrance.
It’s becoming fairly universal in elevators in the U.S. to have a raised star next to the floor button that has a street-level exit. It’s recommended by the Americans with Disabilities Act.
To further complicate things, I’ve seen a very few buildings that have a mezzanine level in between one or more floors.