"Signal generator" is a broad term, but it's commonly used to describe an RF sinewave generator. It's output level is typically given as dBm into 50 or 75 ohms. 20 dBm is a common maximum level.
A function generator typically gives you a choice of waveforms such as sine, square, triangle, and sawtooth, and is typically limited to several MHz maximum. It's output level is usually given in volts peak-to-peak, or volts RMS into no load or into 50 ohms (read data sheet carefully). Some instruments allow you to specify dBm, but that's less common. 20V peak-to-peak into no load (10Vpp into 50 ohms) is a common maximum level. You can calculate the watts from that.
4 watts is more than most RF signal generators or function generators. Maybe you can find a special "high output level" generator, or add a power amplifier.