Not wanting to start a war here, just wanting to keep things 'straight'.
The decks most commonly found under a 1650 are a 44A or a 50A. However you might see a 48" or 42", or even a 38" under them........
While a 44C or 50C will 'fit' under a 800/1000/1200/1250/1450/1650, they were never offered that way from the dealer. The 44C and 50C decks were first 'released' on the '82' series tractors...reason being the 82 series tractors PTO clutch uses/accepts a 5/8" belt, and the 82 series mule drive pullies and the 'C' decks also use the 5/8" belt on the drive pulley.
Also the 'C' decks have slightly different attachment points compared to the 'A' decks, thus a wider front hanger mounting plate on the 'C's to accomodate the different lift carriage.
The 'A' decks used a 1/2" size belt....you can use a 'C' deck on a pre 82 series tractor, as long as you change the drive pulley to the 1/2" size, and move the front hangers accordingly. I imagine a guy could run a 1/2" belt in the 5/8" pulley...how good it would work, and/or how long it would last is questionable at best.
'C' decks -did not- always have front wheels...I owned a 44C that did not have the front wheels, and currently own a 50C that also does not have front wheels.
Front wheel kits (exactly like the front wheels Fordlords pictured) are still obtainable from a Cub Cadet dealer (about $100), and you can weld them on any 44A, 44C, 50A or 50C. So going by front wheels or the lack there of, is not a good indicator of an A-vs-C deck.