TromboneChat

What horns or bell sections fit on shires slides?
What other brands?

Technically none, the shires tenon and threads are their own. But Bach and Edwards are very close and sometimes fit ok.

My Bach bass has accepted two different Shires "L" (Bach-length) slides with a good friction fit. However, the nut on the Bach ran out of threads before securing the slide - with the nut tightened all the way, the slide could still slip out of position and become fully loose. I used it that way for several years but it was risky when the valves were recently oiled and/or I had a heavy mute in.
My tech added some wire so that the nut wouldn't go so far down and enlarged the outside of the nut (using part of a tuba piston valve cap) for extra leverage, and now it all works great (and I can still use a Bach slide).

I'm sure it depends on the horn, both slides are about 1/8" from bottoming out in the socket, so it wouldn't take much of a variation for them to not have a friction fit.

YMMV

It's also very easy to put on an Edwards tenon that will fit Bach, or the other way around. I've done it several times.

Pic of my mod (attached jpg)