I wouldn't make a caramel with butter. I would add the butter once my caramel is ready, to stop it from cooking further. I think butter would burn before the sugar becomes caramel.
Good reasons to put butter/oil in caramel:
Butter/oil comes in handy for coating nuts as it helps with them not sticking to one another.
The fat can also prevent humidity from ...
Well, I'd say it has mostly to do with texture, but also with taste.
To my knowledge there are three basic methods to making caramel:
dry: without anything but sugar. In my opinion the most difficult method, as it tends to burn easily.
wet: with water added to make sugar syrup, which is then turned into caramel. The water evaporates during the process. ...