Is there a generic name for public transport interchanges?

As others have mentioned, "station" is the best word to use if you're just talking about ground transportation. However, if you're throwing air and water transportation into the mix, there's simply not a common term for that in American English. I'm afraid there's no way to get around putting in a sentence explicitly describing the set of things you're talking about.

You could refer to them all as transport hubs, or even just hubs.

From my familiarity with the Philadelphia transit system...

A "stop" is just a place you can get on a bus. It typically has a bench, a sign, and perhaps a very small covered area.

A "station" is a place you can get on a train. It typically has an actual enclosed building, as well as some small amount of parking. At least part of the day it is staffed. I could see where some smaller commuter trains (eg: streetcars) might stop at places that just qualify as "stops" though.

A "terminal" is a place where multiple transit lines end. For a bus system, this is usually a main hub, and has a largish climate controlled building. For a train system, this is usually much nicer and larger. The one in Philidelphia has entire shopping mall attached to it (or it is attached to a shopping mall, depending on how you want to look at it). For airplanes, a "terminal" generally refers to a secured area or wing of an airport.

There is not any common word in use in American English. For bus or train stations, you can often use transit station, however this does not apply to many other public transport interchanges.

I can't think of a single word which encompasses all the things you want. A station needs some kind of building, normally. But a stop is anywhere that the vehicle stops and people can get on or off. Trains almost always stop in stations but buses can stop anywhere. So I'd say the most generic term would be a stop.