Yes, without a doubt, big one is wheel cutting (topping, or rounding-up) machine.
Wheel to be cut would be fitted between two vertical points and the cutter would be on the horizontal spindle propelled by a big hand wheel.
This machine was used mainly on watch wheels for either correcting the form of the teeth or reducing the full form of the teeth to improve the depthing in a train of wheels.
The other one is called Jacot tool - it is used for polishing pivot ends.
Chris