Short Answer: druids learn their spells from a divine source
The divine source of druidic spells is usually characterized as "the divine essence of nature", but it could be directly from a god of nature (like Sylvanus of the Forgotten Realms).
p.64 PHB (Power of Nature)
Druids revere nature above all, getting their spells and other magical
powers either from the force of nature itself or from a nature deity.
Whatever spell they wish to choose will, or won't, be granted to them via either their deity or "the force of nature itself." It's up to the DM to choose to curtail any such choice, or not to.
My question: do druids have full access to their entire spell list
when it comes time to switch out?
Yes. There is no specific rule that limits the druid to less than that list, so the list on PHB p. 208 is the general rule of "what's available" to include more spells being available if they are druids who choose "The Circle of the Land." (PHB. 68) Depending upon which circle the druid chooses, other spells are available, and always "prepared" as a default. See also Specific beats General (PHB p. 7).
The game distinguishes between divine casters and arcane casters
Regarding your concern about wizards versus druids: druids and wizards get their spells differently due to being different kinds of spell casters. Wizards (a particular kind of arcane caster) get their spells through learning. Divine casters get their magic, and their spells, through prayer or otherwise communing with some divine conduit to the Weave, to include "the divine essence of nature" itself.
All magic depends on the Weave, though different kinds of magic access
it in a variety of ways. The spells of wizards, warlocks, sorcerers,
and bards are commonly called arcane magic. These spells rely on
an understanding - learned or intuitive - of the workings of the
The spells of clerics, druids, paladins and rangers are
called divine magic. The spell casters' access to the Weave is
mediated by a divine power - gods, the divine forces of nature, or the
sacred weight of a paladin's oath. (p. 205 PHB)
Different kinds of casters, different ways to get spells. It's not unfair. It is a way that the game designers chose to differentiate the character classes. (You noted that a wizard has access to more spells. Whether this distinction "balances" the classes is beyond the scope of this answer).