The type of rivit depends on the type of the tool in the rivit set, some of them will work with several different types.....
The type of set you in the picture is typical of the ones used for riviting brake shoes, every mechanic in the 30's had one, no one has one today, brake shows come pre rivited...
You can still get just about every type of rivet ever made, but I would hazard a guess the tool was probably for the plain solid core T shaped rivits....