For the FIA what is important is the technical conformitiy of a car to the homologation papers.
There are only two types of E9 BMWs homologated in Group 2 : the 2800CS and the 3.0CSL.
Both homologations were modified several times to allow the cars to progress and to comply with new rules - like the new Gr2 set of rules of 1976.
The 2800CS was homologated on 28 Feb 1969 (homologation #1558 and subsequently also #1585 and #5384).
The 3.0CSL was homologated in November 1972, but most of the first important modifications were added on March 1st 1973.
Before 1972 all cars were raced as 2800CS Gr2, even if they were 3.0cs or 3.0csl with alloy panels removed.
From 1973 all cars were raced as 30CSL, even if they were ex-2800CS Gr2 or 3.0CS/CSi built to CSL spec.
Chassis number was a non-issue for the FIA at that time and it is interesting to note that the reference chassis number on the 1st page of the homologation of the CSL is 2 210 001 - a 3.0CS chassis number.
A number of cars started their lives as 2800cs, were raced by Alpina or Schnitzer in 1970/71 and were eventualy sold to other teams or to privateers after one or two seasons - sometimes in updated form.
In 1973 BMW Motorsport built a batch of special ultralight race shells (about 20 ?), with many modifications : stiffening, different rear supension mounting points, central location for the windscreen wiper, ….
These shells were used over the years for all Motorspost cars, but a also a few were sold to the “tuners”:
the last 12v Alpina (raced end of 73, 74 in orange and 77 in green Gösser livery),
the last 12v Schnitzer (built in 1976),
the two UFO Luigis of 1977.
Most other race CSLs were either updated 2800CS Gr2s from 1970-71-72 or early CSLs with VINs from the 2211-2212 series.
Only a handful of 2275 chassis were used for race cars.
A few examples:
In 1972 the Schnitzer of Alain Peltier, the Dutch Alimpo Alpina, the Luigi Marabout and the Broadspeed CSL had CSL VINs. They all had to be converted to normal CS with steel doors and bonnets (because of this the Golf yellow car of Peltier had white doors and bonnets in the first race of 1972 in Monza).
On the contrary I am pretty sure that the only car raced by Schnitzer in 1973 had a non-CSL schell.
The same year the Alpina "Wyborowa" CSL owned and raced by Walter Brun was in fact an old Schnitzer 2800cs updated by Alpina
In 1974 the Alpina CSL raced by Müller/Ogrodowcyk was an ex Alpina 2800CS.
In 1976 the winner of Gr2 at Le Mans and the winner of the SPA 24h were both CSLs built from non-CSL shells.