What does marking like "aq/ar" on the sprocket mean?
This has nothing to do with dates.
Shimano introduced cassettes on their road racing groupsets first. I.e. Dura-Ace. The first Deore XT lacked this.
The first Shimano MTB cassette was CS-M732:
https://si.shimano.com/api/publish/storage/pdf/en/ev/CS-M732/EV-CS-M732-0969.pdf
This had
B-type: 12-14-16-18-21-24-28T
C-type: 13-15-17-20-23-26-30T
Not sure what A-type was.
Anyway, they made lots of cassettes so 26 letters wasn't enough so they switched to two letters. (And I think it's MTB-specific, for cassettes, road cassettes do without them)
Chainrings had a similar thing - at one time they had 3 types for road, A, B and C
https://www.thetallcyclist.com/2013/01/the-truth-about-the-shimano-a-and-b-type-chainrings/
But now they use a two letter code
https://si.shimano.com/api/publish/storage/pdf/en/ev/FC-9000/EV-FC-9000-3325B.pdf
The code represents the entire set of sprockets or chainrings, and is significant because of 'hyperglide', i.e. the ramps on the sprocket or chainring. The number of ramps is equal to the gap to the next sprocket or chainring, for efficient shifting (if you fit a sprocket designed for a different larger sprocket, then shift performance from that sprocket will be poor). Technically a chainring or sprocket could be defined in terms of the larger ring/sprocket that it shifts to, but I guess writing '34/50' on a 30t chainring is more confusing than writing 34 MA.
An 11t (or whatever) sprocket may have multiple codes because there may be multiple 11-13.... cassettes for a given speed (the letters are specific both to the gear range and the number of speeds (so a 50/39/30 triple chainset had a different code for 10-speed rings than 9-speed).
Sprockets with the same codes should be interchangeable across cassettes (so you could fit an XTR sprocket with the correct code to your cheap cassette), but materials/weight differences are present. Shimano have lots of incompatible chainring designs OTOH and I suspect that chainrings of the same fitment have the same code, e.g., R9100 chainrings are incompatible with 9000 chainrings, and the former for 50-34 are marked 'MS', the latter 'MA'. The cheaper RS510 chainset also uses 'MS' for 50-34, so likely would fit to Dura-Ace and vice versa (though the RS510 rings are much heavier).
If you go through all the chainsets &amp; cassettes on si.shimano.com you could come up with a list, but it doesn't seem particularly worthwhile to do so.
bj is 10 specifically numbered cogs 11-34t, and bk is likewise 11-36t, and for 10 speeds only - a 9-speed 11-36t is called CB (11-36t 9-speed was introduced after 10-speed 11-36t, so this is simply a matter of going up in increments of one letter for each new pattern Shimano made, across all speeds. 11-36t 9-speed cb is just the same as 11-34t au but with the 34t switched for a 36t, and since there were many 9-speed cassettes made before 11-36t was a thing, probably you won't find 'cb' on many 9-speed sprockets, but they are identical to 'au' except the last two cogs.)