The gigs where I get no set list are interesting- after playing for a long time, I just know a lot of songs, or have heard a popular song enough that I know the form and the changes already, and if I can hear the changes in my head, playing them is not a problem. The really interesting bit though is if its a song I've never heard at all. Then, its a game of asking a few questions (what's the key, what's the feel), maybe someone will say it starts on scale degree IV, so you know there's going to be an intro and into the first verse, and you know thats scale degree I probably. Then, you just have to kind of guess your way through the first verse, but you're memorizing the verse at the same time, and usually the second one there's no guessing. And so on. There's also a great deal of watching peoples hands and bodies because there are tells when something is about to happen, and you just get a sense of what they mean.
So there's obviously rote knowledge of music, but there's also this subtext of guessing and watching and listening and mimicry that are a huge part of what is actually going on. The older I get, the more I enjoy thinking about that aspect of making live music.