Please confirm if I identified this BMW differential correctly.

I got the differential for free from Sean while helping clean up a bit during the Suprang adventure.

Based on the information I was able to find on the internet, this seems to be a:

Medium case housing, P/N 1210411, with Limited Slip and 3.73 gears out of an E34 5 series. 

To swap it into my E36, I'd need a different rear cover, and possibly axle stubs, and that's it.

How close am I to correct?

In reply to Brett_Murphy (Agent of Chaos) :

You and Michael did well from Sean.  Just so everyone is aware Sean was basically like Patrick is.  He wanted stuff gone and if it wasn't something he needed for his cars you could have it free.   Not saying show up to his house looking for free stuff but he was very generous with GRM folks helping him clean out his shed and garage. 

That looks like an E30 differential to me based on the ratio, possibly with an E28 rear cover. Some quick searching shows that this style of diff may have come on small motor E34's but if you look at an E36 diff the mounts on the actual case are quite a bit different. As far as the internals go it's a 188 diff so you may be able to swap that into your car if the ratio is good. The S3.73 usually came in an E30 325is and is popular with the E28 crowd to replace the stock 3.25 ratio with.

An LSD diff for an E30 or E28 is worth decent money these days so you may be able to sell it and buy what you need.

Yep, 3.73 LSD for sure. As noted, looks like an e30 diff with the rear cover changed. That ratio is fairly common on e30s (I have the same one on the rally car). 

irish44j (Forum Supporter) said:

Yep, 3.73 LSD for sure. As noted, looks like an e30 diff with the rear cover changed. That ratio is fairly common on e30s (I have the same one on the rally car). 

This. 

I actually have one sitting in the garage with the e30 cover. 

Thanks for the input and confirmation, everybody. I appreciate it. I had to give it a few light taps with a hammer to get it moving again, but once I did it spins freely. That and cleaning the tag off to be able to read it is all I've done so far.