Both are not the same and the MR is better than the Live AR and the Live AR with mic on is better than the one with mic off.
An MR will usually be the instrumental some backing vocals and guide for singing. A live AR is a fully recorded performance that’s used as a playback. The members may or may not have their mic’s on. This is why “hearing a dual sound” doesn’t automatically mean it’s not LIVE AR.
Btw I’m basing this on my own favs like EXO their solos etc.
The cue sheet called some exo performance a live AR but in the performance they’re clearly singing. Initially everyone brushed it off as the fans are lying to themselves or the antis are being hateful lol. But the truth is it’s entirely possible for your favs to have their mic on and still use a LIVE AR.
In fact this is one of the most common “live” singing you hear in kpop.
Personally for me I don’t consider live AR’s live singing even tho I’ve enjoyed many of EXO’s performances where I can hear their vocals. But yeah I know and acknowledge that a live AR with Mic on is not the same as live singing with an MR