A whole bunch of problems can be set up either way. MILP always has an objective, and the constraints are always linear combinations of the decisions. Gurobi is so incredibly fast that it might be worth contorting your problem into a MILP just so you can get solutions at all.

CP-SAT is integer only, so I'm guessing for physics it's not great (you can scale your reals but that's not as good as working with floating point directly).

The advantage of CP-SAT is that it handles boolean and integer variables and constraints much more efficiently than a MIP solver, specially higher-level constraints like all_different.

I would assume largely similarly? https://www.amazon.com/gp/product/1107658799/ is the book I last went through on this and it covers a lot of the same ideas. In particular, I'm assuming the section of this post that aims to minimize some value are directly using the same stuff.