Punch-in
Dropping into record partway through a track that is already playing, so that only the botched passage is replaced and the rest of the take survives.
On a multitrack tape machine this was a craft: the musician played along from a little before the mistake, and the engineer hit record at exactly the right moment and released it just as precisely afterwards. Half a second off and the good note that followed was erased for good. The British call it a drop-in. Later tape machines and every DAW offer auto-punch, where the in and out points are set beforehand and the machine handles the switch.
Pre-roll — playback starting a few bars before the punch point — gives the player time to lock into tempo and feel. Without latency compensation the new audio lands a few milliseconds late, which shows up as a doubling at the edit. With unlimited undo, punching in has largely given way to comping.