Suppose a druid wild shapes into a giant toad. The giant toad's statblock states:
[...] The toad makes one bite attack against a Medium or smaller target it is grappling. If the attack hits, the target is swallowed, and the grapple ends. The swallowed target is [...]
Can the druid bite the grappled target again and not swallow the target? Would the toad have to release the target before biting again? And if so, are there any advantages/disadvantages for the target or toad?
The attacks listed in a monster statblock represent separate options that it has.
If the Swallow attack succeeds, the toad must swallow the victim. It says, very plainly, "if the attack hits, the target is swallowed."
However, it still has the Bite attack, which has a 5' reach (which the victim is definitely inside) and this restriction:
Until this grapple ends, the target is restrained, and the toad can't bite another target.
This implies that it can bite the target it's already holding (and in fact it has to in order to swallow them, since that uses a bite attack). This attack would have advantage since the target is restrained.
Note that even if one ruled the other way (that using Bite against an already-grappled target would automatically be an attempt to Swallow), the toad could still just release them and immediately Bite again. However, in that case the creature wouldn't be restrained.
Note also that if the toad bites a creature too big for it to swallow, it does still get to grapple and restrain it, and could bite it again on subsequent turns.
Nothing prevents the toad from making a second bite attack against a grappled and restrained creature. If a Bite hits, the target is grappled but can try to escape using grappling mechanics on its turn. This same bite attack could be repeated indefinitely. The only limitation to bite is that the Toad cannot bite a different creature than the one that is grappled.
Swallow is a separate attack option. It can (not must) be used against a grappled creature. Note that the Toad has an animal's Intelligence of 2, so advanced combat tactics are probably not its forte. Against normal creatures it would probably swallow them. It would probably release a Fire Elemental that it bit (well, if you could actually grapple a Fire Elemental, but you get the idea).
Note also that the Toad also doesn't have to maintain the grapple. The grapple-ending condition by a grappler is (from the Basic Rules):
you can release the target whenever you like (no action required).
