Is it ok to leave the stick lead and the tig torch hooked up to the
same terminal all the time, or do I have to swap them out?

I expect to use this mostly for tig.

I've left both cables hooked up for years. I do hang it so the stinger
doesn't lay on the ground and accidently arc to something. Same with the
TIG torch when I'm not using it. I dunno, maybe switching to TIG unpowers
the stick and vice versa, I've never checked. I've only had it for ten
years.

Of course, you use the same ground cable anyway.

Karl