There’s a cross-over. A narrow-brimmed fedora can also be called a trilby, but not all trilbys are fedoras – this tweed one, for instance.
Are you sure they’re not homburgs. Where I live, in the '60s, you couldn’t wear a suit without a homburg. It was kinda the defining characteristic of my father’s generation.
Not much to add, other than, when I think of “homburg,” I think of Mr. Drysdale, although in a couple of eps I think he wore a trilby or something similar.
I had the impression that a Trilby was either just what the Limeys called a Fedora, or it was the name of the kind of old-man fedora worn by Bear Bryant.
I’ve been wearing a fedora every time I left the house for twenty years. Every couple of years somebody tells me that they’re coming back in style, or that some sector of the culture has taken them on as their signature. I have yet to see it really happen. I don’t know why. I’ve never heard from anybody that they don’t like the look of a fly brim. But it never seems to happen, and I suspect somebody at Hatco just puts out the now and then to see if it’ll stick.
Porkpie hats were trendy in the 80s too, prompting this Rank and File lyric poking fun at East Village hipsters:
*
Did you ever see a sheep in a porkpie hat?
Ever see a lemming dressed all in black?
You might have been there but I’ll tell you just in case
Just take a walk down St. Mark’s Place*
I call all the hats hipsters wear “douchehats,” but that might not be the technical term. 
Ah, a Londoner whose dad worked in the City. He also carried a tightly-rolled umbrella. No guess, just a familiarity with 60-70s TV.
I associate porkpie hats with Mickey Spillaine. Mike Hammer wore one long after they stopped being stylish (were they ever stylish?).
Another name for them is “Stenjers”.
“And you think you’re immune
But I can sell you anything
Anything from a thin safety pin
To a pork pie hat”
Joe Jackson - I’m The Man
I have to laugh a little bit, because these have been popular on college campuses for at least, oh…at least 25 years. I don’t think they ever really go out of style; people just grow out of them, or something. (I love hats and don’t care who’s wearing what, either)
When I lived in NYC in 1979 and started my first job, I was kind of surprised to see so many guys wearing hats, but only men who went into the building where I worked.
Took me a few days to realize The Cloth Hat, Cap and Millinery Workers International Union (CHCMW) was on the floor above where I worked.
From that experience, I knew exactly what hat you were referring to in the OP.
Don’t know if that union still exists, or if they still have an entire floor in that NYC building, but I certainly saw lots of styles of hats for men on guys going in and out of the building, but you could tell it was sadly a dying trade in the city.
Dude. I seriously came in here to post the exact same thing.
Douche.
I like how you are wishing to be able to follow a trend so that you can not feel like a trendy douchebag. 
That’s pretty comical.
Ironically, it’ll only make people think you’re a wannabe that doesn’t realize he’s out-of-date. And of course explaining that you’ve always been into the look will sound exactly like a spiel any of those conformos might give. You can’t win. You’ll just have to be what you are, and deal with the fact that others don’t understand.
Well anyone who wasn’t a trendy hipster would dress how they like whether or not it’s in fashion. Only trendy hipsters avoid doing something they like BECAUSE it’s currently in fashion. Those hats come in and out of style every 15 years or so. So you’ll spend your entire life on a cycle of having your fashion be the trend, or being just out of style.
This is a fedora.
The itty-bitty striped jobs are more properly called “fedorkas.”
Dude are you trying to laugh WITH or laugh AT me? Fwiw, I wear what I want to wear, even if I look around and see hipster douchebags wearing Timberlake wannabee hats. Even trying to attempt to be a trendy hipster is so unavailable to me that it is not even an issue…thanks for the support, though.
I guess that depends on your sense of humor and self-assessment doesn’t it?
Something I’ve noticed from being around hipsters is that no one likes to diss hipsters more than a hipster. From where I’m at it simply doesn’t matter. Dress how you like. Sure someone might look at you as a hipster, but whatever. Why are you so concerned about it in the first place?
And how does being a hipster become available to one? Do they not sell indy-rock, breakbeats, or underground Hip Hop in your area?
Wow, never mind. You aren’t worth it. It must be great have such a pure, focused sense of self and no self-doubt. You are the man.