Are the handles the main difference between a sauté pan and a brazier like this:
IE, can they be used for the same things?
There's some overlap between the words braizer, casserole, sauteuse, and dutch oven. Different manufacturers apply the names somewhat differently. As a generalization, these are somewhat broad, have a mid height straight side with an abrupt transition to the sidewall and lid. A saute pan will be broader with a flared side and a more rounded transition to the side wall which will be lower.
You'll get somewhat less evaporation of liquids in these sorts of pans compared to a saute pan. These are well suited for wet cooking, but you can certainly sear meat and cook vegetables in it. And you should for preparing the braise all in one pan. While you can do similar things in a saute pan, you can't cover a large cut of meat in a saute pan because the wall is not tall enough. And the lids rarely fit as tightly on a saute pan.
If you cooked a large steak in each pan, the closer higher wall of the brazier would contribute to some steaming effect on the steak. This could impair the crusting of the steak and cook the steak more deeply compared to the saute pan. How pronounced and how detectable the differences are is up to some discussion. All things equal, the steak in the saute pan should be superior.
Each pan has it's uses and while there are times you could use one for the other, there are times you shouldn't.