I looked at Kester's catalog online (PDF), they only list two basic materials for Kester 44, SN63Pb37 SN60Pb40 SN = Tin Pb = Lead.
That would account for part of the product numbers, I would think that all other part numbers would account for the package size.
Does this help?
Hey, give Kester a call and ask them what would they use.....

...
or... what their part numbers mean.
1 (800) 2-Kester (1(800) 253-7837)