If you dry off the floor and the base of the toilet and then don't use the toilet for a while, does the water come back? If it does, then the problem is not in your wax seal. If it stays dry until you flush it, then the wax seal may be your problem.
For the first scenario, where the water leaks even when the toilet isn't being used: You could be leaking from where the supply line screws into your fill valve, or from the large thin nut that secures the fill valve. Or you could be leaking from higher up.
For the second scenario, where it only leaks when you flush the toilet: It can be the gasket between the tank and the bowl that is leaking or the wax ring is still not sealing for some reason.