This particular buzz was a ground loop problem with the recording equipment, so it's a small hum. Using Noise Gate doesn't work because it can only take it out where there's no other sounds. Someone once told me there was a way to do it where you could record the noise you want to remove, and then somehow use that to cancel it out from the original audio? Would this work, and if so what's this method called? Is this built into Logic or is there a plugin for it. Sorry, I'm not very experienced with sound design so I don't really know what I'm doing, and we don't have time to re-record this audio. There's also some audio with static from the camera it was recorded with, and that would be nice to be able to remove, but this is higher priority. Thanks.
The process you describe recording the hum sound and then cancelling out the hum on your recorded track is called phase cancellation. Both tracks would have to be exactly the same in regards to volume level and timing and this is achieved by reversing the phase on one track. I doubt this would work for this, but for this type of issue I use Izotope RX4, a plug-in with stand-alone application (can be used outside your DAW) for post production which has de-hum, de-crackle, de-noise & de-click features. It allows you to repair audio where these types of artifacts can be easily removed without effecting the recorded tracks. - Hope this helps.
You can try using Logic's Match EQ plugin to isolate / reduce the buzz frequencies if there's a section of the audio that's only buzz... have the EQ "learn" the frequencies in that section, then use a negative "Apply" value to notch out the values.
There are two different types of noise removal software: graphical-based and knob/slider-based.
As you've might've seen, knob/slider-based denoisers are typically bundled with DAW's because of their speed and light CPU use when using them in real-time and they're pretty straight forward. Define the timbre of noise for the denoiser to look for and set a threshold level that activates the noise removal.
Graphical-based denoisers on the other hand are much more powerful and precise in the reduction process as for their removal algorithm is based purely on impulses whose timbre closely resembles the noise in the audio that you wish to remove.
You can try your stab at real-time noise removal but since you're further tweaking the audio in post-production, I'd get my hands on an offline, standalone piece of software. They definitely don't come cheap, however, getting your hands on an offline denoiser will cost you at least $100. An alternative you could try is Audacity's noise removal effect as for it also uses noise impulses to isolate and remove unwanted frequencies.