The Schwinn bottom bracket (yes, it's called a bottom bracket) set is indeed 28tpi threading.
24tpi is more common, used on most one piece cranks, and undoubtedly is the 'cheapo' set you were quoted.
28tpi is ALSO used on higher end 'old school' bmx cranks and BBs. The bottom bracket sets available in 28tpi are better quality, usually Tange. Not exactly 'Schwinn specific' but 'Schwinn compatible'...At least they knew there was a difference- I'd shop at that place!
Old Schwinn BBs are very good quality and usually last and last. Good used ones show up on on Ebay. :wink:
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FWIW, the new 28tpi Tange BB, even though it's the same thread as old school bmx, usually won't fit an old school Sugino crank, but the Schwinn parts will. For some reason they won't 'make the turn' on that particular one piece crank and the first threads can't start... :?