Discussing the difference between cryptids and folklore and it's not strictly an antiquity/modernity thing but I feel like the hard dividing line might be the invention of photography. The telling of cryptid stories thrives on and revolves around positive proof or lack thereof, their payoff requires documentation in a way folklore never does or is expected to.
Though Hannivers and other hoaxes like that predate the 19th century, so there's some grey areas to it.