There are actually quite a few similarities between the instruments.

If someone learns how to play bugle calls on one, they'll be able to do it on another pretty easily. I think it's probably easier to go from Trumpet/Bugle to Trombone rather than the other way around, though. It has to do with the necessary embouchure for the two instruments - trumpet/bugle is a little more compressed.

Even though trumpet is my primary instrument, I can pick up a trombone and make a recognizable melody emerge from the bell. But, I understand the methodology behind the brass instruments and can apply it to the brass family.

(I surprised many people in my home town when I didn't become a music major in college.)