Yeah, on a trumpet you can play multiple notes with the same fingering. The set of notes you can play with a fixed fingering comes from the harmonic series. A bugle is essentially a trumpet with a fixed length of tubing, and famous bugle calls like Reveille and Taps all come from that harmonic series (and can also be played on a trumpet without varying the valves).

My understanding of how this works is that the length of the trumpet's tubing (at any given fingering) permits the air to resonate in standing waves only at one of the frequencies in a harmonic series. The player's lips can vibrate at any frequency on their own, but the big column of air inside the trumpet will essentially lock the column of air into vibrating at the closest frequency in that set.