my point is that the classes' names are arbitrary categorisations made for the players. they don't exist to that degree in universe.
it's not like characters have the name of their class stamped on their forehead.
Technically, they do.
You can see this in various forms of media. Like the DnD film where the MC identified himself as a Bard. They saught out the help of someone who is identified as a Paladin. There was someone identified as a Wizard.
Even in BG3, we see this. People explicitly acknowledge you as a Druid. Gale will identify whether you're a Sorcerer or a Wizard.
BG3 doesn't offer the most drastic of differences between Druid and Nature Cleric, but even so it's still there.
Nature Cleric explicitly is devout and gains their abilities from their deity (Which may or may not be Silvanus), while a Druid may not care about any deity at all (For example, the Shadow Druids) and simply have a connection to nature in some form.
Here's an excerpt from 5e PHB in regards to Nature Domain:
"Gods of nature are as varied as the natural world itself; from inscrutable gods of the deep forests (such as Silvanus, Obad-Hai, Chislev, Balinor, and Pan) to friendly deities associated with particular springs and groves (such as Eldath). Druids revere nature as a whole and might serve one of these deities, practicing mysterious rites and reciting all-but-forgotten prayers in their own secret tongue. But many of these gods have clerics as well, champions who take a more active role in advancing the interests of a particular nature god. These clerics might hunt the evil monstrosities that despoil the woodlands, bless the harvest of the faithful, or wither the crops of those who anger their gods."
