A noise gate is a kind of triggered On/Off switch. You set the threshold to decide the minimum signal that you want to pass to the amp. Any time the signal into the box drops below that set value, the output shuts off. This is especially useful for single-coil pickup guitars. You can adjust the threshold so that hum is blocked, but the signal path opens up when you're playing. The downside is that quiet playing either gets blocked by the gate, or gets lost in the hum. You might see this as a loss of sustain, because any signal below the threshold setting will be shut off, whether you're holding a note or not.

A compressor reduces the volume difference between loud and quiet signals. The volume of a low-level signal will get boosted, while loud signals get rolled off. This can add sustain by increasing the volume as a note fades away, but it will also boost any noise in the signal.

You can combine these boxes if you're willing to spend some time experimenting with the settings. Start with just the noise gate. Set it it so that it just shuts off the noise, while passing quiet picking. Then put the compressor between the noise gate and your amp. Adjust it to get the sustain you want, while setting the release to minimize the noise that follows each note. If the attack and release settings are extreme, you will get a problem called 'breathing', where you can hear the compressor working.

You can try putting the compressor in front of the noise gate, but I think you will find its more difficult to get rid of the noise without hearing the gate working, much like the 'breathing' problem with the compressor.