I vaguely remember that 100μF represent the capacity of a capacitor, but I also kinda remember that it has to do with the voltage. So my question is, do 10V 100μF and 16V 100μF capacitors have the same capacity and output (meaning does the 16V 100μF capacitor is the same as 10V 100μF capacitor only capable of working in a higher voltage system)?
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).
Up to 10 V, both capacitors behave as a 100μF capacitor.
Between 10 V and 16 V, the 10 V capacitor may behave as a capacitor for a while, but it may increase its leakage current, it may go off with a bang, we just don't know. The 16 V capacitor will continue to behave like a capacitor.
Above 16 V, neither capacitor can be trusted.
Assuming (from the high capacitance) you are talking about polarized caps, then yes, both will behave pretty much the same below 10V.
That you remember a correlation with the cap's voltage might be due to the fact that ceramic caps DO change behaviour with voltage. A ceramic cap loses capacitance with increasing voltage. Depending on the dielectric, you might have only something like 20% of the rated capacity at full voltage (at least for X5R, others can be better). So a higher voltage rating will give you more capacitance at your working voltage.