If I'm at the computer, I dedicate a much smaller amount of time trying to self-solve a problem than I would on a walk. If I can't work something out in like 20 min, I'll try googling around for a paper which answers the problem. So there's a difference in time/effort expended on independent work. I'll try to work things out explicitly, like find examples and such.
When walking I don't (usually) have a pen nor paper, and so explicit examples aren't possible, and I don't pull out my phone to google or anything, so I'll work more abstractly due to those constraints (and probably less precise…