Pay Over Time is a new "feature", which traditionally was not possible on an Amex card. Technically speaking, if we want to be pedantic, American Express is a banking and finance entity and offers many account types including typical credit cards (American Express Blue, any of the branded Amex like the Delta or Hilton Amex).
The traditional American Express card, though, is a charge card and not-withstanding the new Pay Over Time "feature", requires the entire balance to be paid in full every billing cycle. The entire reason they're popular with businesses is it provides an easy way to effectively do Net 30 payment terms without having to deal with POs and invoicing.
The primary reason Amex customers are more valuable is because most Amex cards carry an annual fee, which only more affluent folks can afford.