A "live set" typically involves the performer playing synths and programming the drums live. There are no record players, no pre-recorded tracks, everything is played live on the fly. Example: https://youtu.be/cVFzblT5VPE?t=4177 (a daytime one so you can see the gear)
With a "DJ set", the DJ is playing two or more tracks, beatmatching them and mixing them together, transitioning from one track to the next. This still takes a lot of skill. If you see two or more turntables or media players and a mixer in the middle, that's a DJ set. Often the DJ brings their tracks to the venue loaded on a USB stick and plugs it into the media player. Just because there's a USB stick present doesn't mean the DJ set was pre-recorded. Example: https://youtu.be/Ubyd98XV5C0?t=1018
The scene is notorious for it. It's really not hard to find vids of DJs dancing, pointing, posing, and poking uselessly at a mixer which is obviously just there for the look.