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.
if you met someone who lives in the woods, worships silvanus, casts druid spells, *really* loves nature... you would call that a druid.
just like if i met someone with a white coat working in a hospital and giving medicine to people i would call it a doctor.
i don't check his degree in medicine or care if actually he's a "herbalist with a specialization in hospital doctor stuff"
Except, druids and nature clerics have a completely different lifestyle. Not only is their actual worship tradition different (druids don't worship one god in particular per default), they have different living arrangements (circle vs solitary), different dominance hierarchies (only so many arch druids), etc.
If a nature cleric is the same as a druid, a Paladin is the same as a cleric. Clerics don't smite and clerics don't wildshape. There is a good reason for both if you look at the fine print.
Paladins are more martial and less versatile than clerics. They serve a cause above being loyal to a god. Druids are a far more extreme form of a nature cleric, if you will. Their connection to nature is not based on belief in a specific deity. Worship is a much, much smaller part of their lives, while they're more in tune with animals than humans.