Yup. The 'something on the compressor' is the thermistor (screwed into the back/side) which turns off the compressor to prevent overheating. It looks like a single plug aftermarket version will simply have this built-in so you won't see it. Some digging around indicated manufacturers started moving in this direction (built-in thermistor) some years ago - likely due to lower cost and increased reliability of the thermistor so it didn't need to be easily replaceable. I'll wager a guess if you order a new compressor for an older car at this point it's probably a toss-up which one you'll get (internal vs. external thermistor) which is probably leading to the confusion. I originally thought this was an extra ground wire since there is already a high/low pressure switch cut-off located at the receiver/dryer (which, btw, you are "supposed to" also replace whenever you replace a compressor) but apparently there is a local temperature switch as well (internal or external) - you learn something new every day !
Yeah - what I would do (since I don't like altering the car/engine side wiring unless absolutely necessary) is cut off the plug on the old compressor that connects to the engine wiring harness (leaving at least several inches of lead wire of course). Then cut off the new compressor plug and then just butt-splice the old connector onto the new one. Make sure you get a really good crimp on it - there are a lot of amps moving through this connector and you don't want a poor connection.
Of course this will likely void the warranty. So before I did that I would test fit the compressor and hose connections to verify fitment. I would also bench-test the compressor to confirm it works (search youtube). Isn't DIY fun?
I also poked around to see why your connectors don't match up. It looks like Nissan changed the connector type at some point. My '90 Pathfinder has the white/clear (well - yellow at this age) large blocky connector which is also likely creating confusion in the aftermarket parts market.