Boeing started referring to the original 727 as the -100 shortly after the -200 was announced in mid-1965. Officially (what's on the dataplate), most -100s are designated as 727-22, 727-30, 727-25C etc.
Now here is where it gets confusing. New -100s ordered after Boeing announced the -200 are officially designated as 727-1xx. For example, Pan Am ordered 727s for the Berlin IGS in early 1965 which were designated 727-21s. There was a later order for a few QCs which were designated as 727-121Cs Eastern's QCs, despite being built from late '66 to early '68, were still officially 727-25Cs (QC was a marketing designation) because they were ordered prior the original 727 being redesignated as the -100.
American ordered a few additional -100s along with their first -200 order. These are 727-123s. The bulk of AA
's huge -100 fleet was ordered in the early '60s and were designated as 727-23s, including those from that order built after the -200 became available.