Mac is right on the money.......Pencil, eraser, whiteout. Don't forget yer mutes...Valve Oil, Thermos (Hey, Trumpet players get mighty thirsty on the Bandstand, hahaha)!

As far as terms go, trumpet players do have special terms for different articulations>

Doit> Play the note and rip up a half octave or more.

Shake>In classical parlance, it would be a trill. Commercial players (Jazz, Big Band, Rock) Also call it a trill, or shake. Unlike moving valves (Classical) it is done by moving the tongue up and down. Listen to Maynard Ferguson, Bill Chase, or Doc Severinson and you will get the idea.

Cap>There are many terms for this one. Basically, it means play the note short with an accent.

Half Valve>Play the note with the valves half way down, moving up or down.

If you want to get a better idea of how trumpet and trombone articulations work, check out any chart by Sammy Nestico, and then get the audio files of these charts played by any of the great big bands>Count Basie, Duke Ellington, Woody Herman, Stan Kenton, Buddy Rich, Maynard Ferguson, Rob McConnell, etc.

PM me if you want to see one of these parts.
Hope this helps,
Ed