Do you know what a "priest" is?
It's someone who stands in the role of intercessor between between the gods and ordinary people. The historical druids might have done that, but the D&D druid was never based on historical druids, of which even less was known in the 70s than it is now, but mythical/fictional figures like Merlin and Radagast.
Historical Druid:
Nature magic: No, there is no evidence to tie them specifically to nature magic;
Shapechanging: No, there is no evidence to suggest they believed they could do this;
Intercessor: yes;
Magic: yes. Both the druids and their enemies believed they could wield powerful magic;
D&D 5e class: Cleric.
D&D/CRPG Druid:
Nature magic: yes;
Shapechanging: yes;
Intercessor: no;
Magic: yes;
D&D 5e class: Druid.