A scalp trade can last for as long as a few minutes and a swing trade can be as quick as 1 or 2 days. The biggest difference is that you don’t hold scalp trades overnight (not even for a few hours) while swing positions are held overnight.
In my mind, scalping is differentiated from the others in what the term implies. Scalping is just "taking a little off the top". Which is what Native Americans actually did. They took a little off the top of their victims. So scalping is just grabbing a few ticks. The rest of the terms are time-based. Day for intraday, swing/position for multidays/weeks/months. With those definitions in mind, there cannot be a swing-scalp in that sense, although one could try to scalp a few ticks over many days, by having a 3 tick target with a 1000 tick stop.