My wife and first born both play trumpet, and it turns out this is a B-flat (Bb) instrument.
I'm not classically trained (or trained at all) so when I learnt what this means I was a bit shocked, though eventually I started to understand and I went from saying: "Well that's just ridiculous!" to "Well that's very clever."
There are many different sizes of trumpet, and they all use the same fingering to achieve the "same" notes. That's the fiction that they take part in anyway.
Take two very similarly sized trumpets -- a Bb and a slightly smaller C trumpet. The same combinations of fingering are referred to as the same note. But they are in fact pitch-shifted away from each other. The Bb trumpet with the same fingering will (pretty much) produce a tone that is two semitones lower than a C trumpet. They both refer to the note as "G" (for example), even though it is two semitones higher on the littler C trumpet.
So how does such a crazy notion work in the real world, in orchestras, for example? The horn blower will be handed sheet music that is transposed into a different key! So when they think it's time to play a C, and the pianist hits a Bb chord, it will all sound in tune, and no one will be any the wiser (so long as they only look at their own music!).
And what about in smaller, less organised musical groups? It's no surprise to learn that musicians such as trumpeters get very good at transposing on the fly!
Anyway — the lesson for me is that whatever note (or key) my Bb-Trumpet playing family say they are playing... I just play a note that is two semitones lower (on my 'concert pitch' guitar) and we should be OK.