The primary difference between running a generator and the main engine is the monitoring systems. Generators monitor temps, oil pressure, voltages, etc. If there is problems they shut themselves down. The main engine does not do this; you are responsible for keeping an eye on the gauges. Generators are designed to run unattended while you sleep, go to the beach, or whatever. Set it and forget it!

In my experience it is typically no problem to run a generator while sailing or motoring. If the boat is built to ABYC standards it should be no problem. (And again, it will shut down before it runs out of oil, water, etc.) However, if the charter company asks you not to run it while sailing for whatever reason you should probably respect their request.