JoelOnSoftware had a great piece back in the day where he mentioned that while he consciously knew what a short sale on an option was, in practice he had to stop and think about how to calculate it, while his financial friends just knew the answer immediately. He drew a comparison to pointers in C, where if you're going to be a C programmer, then pointers should just be intuitively obvious to you and not something you need to think about.

IAW, there are no pure fast or slow thinkers, a lot of this is just how well have you internalized the background material. Having quick repartee in conversation has absolutely no relationship to immediately seeing what the loop variable should be in a programming problem. FizzBuzz isn't quickly solved by decent devs because they think faster, it's quickly solved because it's a trivial problem that doesn't require serious thinking for experienced devs.

When I'm programming for finance or medical, I often have to tell the PM "let's stop here and let me think about this for a day". Because it's not my field, it takes me a while to get my head around it. OTOH, there's very often algorithm conversations where I have to wait for others to catch up.

I'm not sure it is quite that simple. The other day someone asked me about the project I've been working on. The thing I touch nearly every single day and know in intimate detail...

It still took me what felt like a good minute or more of thinking to remember anything about it and more than that to recall specific details of interest. It would take me even longer to think about something that I don't have at the tip of my tongue, so to speak, but I find there is no such thing as an immediate answer for me. That doesn't seem to be true of all others.

I think you're hitting on the fact that there are multiple variables that contribute to "quickness." Having digested a lot of background material is definitely part of it and ties to the higher up posts about e.g. Churchill. Also a way intelligence can correspond to it, in the sense that more intelligent people have often digested more topics. But there also seem to be people who are less distractable, more tuned in to what is going on, and more able to tie current happenings to their body of knowledge and make a joke or whatever.