When it comes to Fate, it's a little of column A and a little of column B. Several of the known Beast class spirits are based on actual historical and mythological figures, but just Fate's version of them. Beings like Goetia, Camazotz, Kama and Nero are based on the real life legends (Especially Nero since Proper Human History Nero had people thinking he was the antichrist while he was alive, which also might be why Fate Nero has two different Beast versions) but then there's Fate Originals that are classified as Beasts like Kiara, and some spoiler characters. If you're curious here's the current list of known
ones
But also yeah, like everyone else has posted before me has said as well :V
As for the Grands we don't actually really know who the current ones are. All we know are the ones that
used to be Grands but stepped down to help us as we can't normally summon them, or ones that would
qualify for Grands but haven't accepted the mantle for their own reasons.