With punch-in/punch-out, you have it in playback mode, then it automatically changes over to record at punch-in, then back to playback when it reaches punch-out. It’s especially nice if you have this embedded in a larger playback loop. Then you get a new take on each pass thru the loop.
The traditional use is for the tricky bit of a solo. Here you have this great take except for a slight flub at the tricky part. Instead of having to redo the whole take, you just redo the hard part. When doing so, you need to get in the groove and pick up the feel prior to the punch-in point. That’s the value of it being in playback mode, then switching to record at the critical moment without anyone having to hit record. The first attempt at punch-in is usually bad because you aren’t acclimatized to the situation.
Back in the day, there was tape and a footswitch. You listened to playback, then stomped the footswitch to flip the tape head to record on the track of interest. This obliterated whatever was there before, so no turning back. You also had to stomp the footswitch again to stop the obliteration. And with repeated attempts, the tape would stretch and wear thin, especially if you were running the tape at high speed. Then you lose the whole mix. I did that once in the 1980s, using the cheapest Fostex 4-tracker in the world and metal tape. It helped inspire me to do other things for 30 years, waiting for DAWs to be invented. There was a ray of hope in the 90s with the Yamaha CBX-D5, but I didn’t have the money for it. So poor for so long. We are so unbelievably blessed in this century!