Do 10V 100μF and 16V 100μF capacitors have the same capacity and output?
Consider a glass of water: -


I vaguely remember that 100μF represent the capacity of a capacitor

No, capacity is how much something can be filled without spilling. Capacitance is the term measured in farads and is equivalent to the area of the glass above.
The height in which water is filled is equivalent to the voltage and therefore capacity is capacitance multiplied by voltage. This equals charge i.e. Q = CV.

So my question is, do 10V 100μF and 16V 100μF capacitors have the same
capacity

No they have the same capacitance. Capacity is how full you can safely fill the capacitor and that related to charge (Q = CV).