Say a Wizard casts Find Familiar for himself, and then casts it again into a Ring of Spell Storing. The Ring is then given to another person, let's say a Rogue, who uses the Ring to cast Find Familiar.
The description of Find Familiar says
If you cast this spell while you already have a familiar, you instead cause it to adopt a new form.
but the description of the Ring says
The spell has no effect, other than to be stored in the ring.
What happens? Does the Wizard's familiar change when the spell is cast into the Ring? Does it change when the spell is cast out of the Ring? Does the Rogue get a Familiar, since the Rogue is considered to be casting the spell?
Best Answer
Specific Overrides General
This is a basic "specific overrides general" situation. The Ring of Spell Storing has specific rules that override the general cases for Find Familiar.
When the wizard loads the ring, the specific case of "Casting Find Familiar into a Ring of Spell Storing" overrides the general case of "Casting Find Familiar".
The clause...
...trumps anything the spell might do otherwise.
When the rogue activates the ring, the specific case of "Casting Find Familiar from a Ring of Spell Storing" overrides the general case of "Casting Find Familiar".
...means the Rogue is the caster and gains the familiar, even though the wizard's stats are used. The stats are not really relevant for the spell in question, but it may matter for other spells.
End Result
The Rogue gains a familiar. If it somehow already had one, it changes or reappears as described in the spell.
Side Note
The ring can be loaded by "any creature", but actually using the ring to cast a spell requires attunement.