The animal is right by saying palystes are true spiders.
True spiders fall into the sub order Araneomorphae.
Tarantulas are in the sub order Mygalomorphae(used to be Orthognatha), more primitive
spiders.
The main differences between the two,
Mygalomorph spiders have paraxial chelicerae and 2 pairs of booklungs.
Araneomorph spiders have diaxial chelicerae and 1 pair of booklungs.
Size has nothing to do with it, just look at Cyriocosmus spp.
As for your spider being 20cm, that would be a record by some margin!
I kept a few Rain spiders many years ago and what I thought was an
exceptional female only measured around 13cm.
If you can post pics, please do. That size is hard to believe
cheers