UPDATE 2: This car is now listed on ebay as a "Buy It Now" for $9500*. The seller also messaged me: "Before bought it the car was converted to an automatic and the engine was swapped.
the baur number is: 2331-11" That does explain the engine discrepancy. Thank you, Steve!
UPDATE: Thank you to our friend, Uwe Hinz, for sending us the Baur number for this car: BAUR Nr. 72331-14. Thanks, Uwe! ;) (See comments, below.)
Thanks to Thomas J. for sending me the link to this craigslist ad in CA!
1981 BMW Baur - $9950 (monterey park)
The listing says it is a 4 cylinder, but a VIN check (below) says it should have an M20 2.3L six.