Engine rotating a generator at its rated speed, but engine power exceeds power required?

What would occur if a gasoline engine would be driving a generator (specifically, a permanent-magnet synchronous AC 3-phase sinusoidal generator) as its only load at the output shaft and if that engine is rated at i.e. 35kW @ 8000 RPM but at the same speed the generator is rated to produce 30 kW of electricity, at 120V / 250A?

Is a “rated power” of an internal gasoline engine a rating for its maximum possible power output at a certain RPM? Meaning that if a load (in this case, the generator) requires less power input from the engine then the engine throttle would be positioned as such to allow the required fuel amount to be consumed, but not the maximum safe possible (because it is unnecessary)?

If the load at that speed would be larger (i.e. 35kW, and not 30) then the throttle would need to be opened more to increase the fuel flow to produce the required power?

Or does the engine produce 35kW at 8000 RPM regardless of generator load and the 5kW is unused i.e. dissipated through heat?

Excuse me if this is too simple but I would like to find clarification regarding this.

Thanks