Golden box type tool is for retracting brake calipers. They still make them today. Google "disc brake piston tool". It is similar to the round one you have but the block style is used with a ratchet instead of a clamp tool. You need to apply pressure by hand and turn your ratchet at the same time. The multiple faces are spaced differently to accommodate different caliper piston sizes. The Pistons that require a rotation while compressing are determined by having specific holes in the recess of them 180* apart. These holes are what the tools fit into to allow the user to rotate the piston.
The round style one you would use it with an assortment of adapters and a specific brake caliper tool. But in your case since it has a square provision for a ratchet I believe it is just another variation of the block style type.