I think since there are not enough wires for both switches, yes. The answer would be either you wire both functions to one switch, so the switch turns on both the fan and the light, or the other option is you only wire up one function. Wiring up the functions independently in this case does sound like it’s not an option.
With that being said, we would recommend to document the wire colors and then take a look at this wiring guide. It goes over the standard wiring colors, standard installation, and some other factors. It may help to answer your question about wiring up switches.
Good luck, let us know how you make out!