Here's a definition taht supports the way i learned it on Woodwinds long ago.:

"The trill is a musical ornament consisting of a rapid alternation between two notes (compare tremolo). These notes are usually adjacent on the musical scale. "

Most often, trills are played between 2 adjacent notes in the scale, and the distance may be 1/2 or whole tone, but mostly whole tones.

I played thousands of 'em on teh clarinet over the HS and college years .... we were the "string section" of the band !