Their terminology is odd. The thing you move while playing is generally called the hand slide. There's nearly always a separate tuning slide located in the crook of the bell section.

(Some relatively rare instruments like the Shires Alto do "tuning in slide" with a mechanism for fine adjustment in the hand slide).

If you're also moving the tuning slide in the middle of a piece you're probably a bass trombonist doing the now-impossible glissando (see https://www.youtube.com/watch?v=fWJPeA_1g48) in the Bartok concerto for orchestra.

The trumpet, french horn, tuba, and euphonium also rely on the tuning slide to control pitch, so that's not an accurate statement.

I had the same confusion - I'd move the [...] to the following sentence.

Oh, I read that as an independent statement, rather than one qualifying the first.