I have found it odd that a PC may cast a spell from a Ring of Spell Storing no matter what class they belong to, but a PC must has a spell on their Class' spell list to cast it from a scroll.  This doesn't seem to fit any logic I have.  I guess a DM needs to be extra, extra careful if they want to allow the party to have a Ring of Spell Storing.

Does anyone have an explanation for this other than a game balance reason?  And if it is for game balance, why, how?

Well, for one thing, the ring requires attunement, whereas scrolls don't.

They're completely different items. Why would you expect them to work identically?

Well you see, the ring contains the magic within itself, ready to be released by following the casting instructions, whereas a scroll simply contains the magic within itself, ready to be released by following the casting instructions.

There are a few reasons :)

1) They are completely different items so you wouldn't expect them to necessarily work the same.

2) The ring contains the ACTUAL spell. In order for the ring to contain a spell someone has to cast that spell into the ring. The person attuned to the ring is just releasing the stored result of the spell casting. This is why they don't need to know the spell or have it on their spell list or even be a spell caster ... because someone ELSE actually cast the spell into the ring.

Putting a spell into the ring requires the spellcaster to expend a spell slot and putting it into the ring only requires as long as casting the spell. Just an action or 6 seconds in many cases.

3) However, a scroll contains some sort of written form of the spell that is stored there by "scribing" not casting. It clearly does not use the same process as a ring of spell storing. Placing a first level spell on a scroll requires 1 day and 25gp plus any material components required.

"With time and patience, a spellcaster can transfer a spell to a scroll, creating a spell scroll. Resources: Scribing a spell scroll takes an amount of time and money related to the level of the spell the character wants to scribe, as shown in the Spell Scroll Costs table."

Scribing a spell does not require a spell slot to be expended.

It is reasonable to think that the information scribed on a scroll is only really intelligible to someone who might one day be able to cast that spell. It could simply be part of the magical process used to create the scroll.

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Given the completely different processes involved in putting a spell into a ring of spell storing compared to scribing a scroll, there is no reason to expect that the mechanics in terms of who can cast the spells from the different magic items would be the same or similar.

Finally, :) , how it works in your game or the games you play in is entirely up to the DM but personally I have no problem with justifying different behavior for a ring of spell storing and a scroll.

As an example,

A PC that was going to use a Scroll with Find Steed on it, would have to be one of the few (one?) classes that can cast that spell.

But, if a Paladin loads up a Ring of Spell Storing with a Find Steed spell, anyone can cast that spell.

It just seems that both should be usable by different classes in the same way, and I can't really see a justification for it not working like that, except that for play balance the developers wanted to protect several spells that "belong" to one or a small class of characters.

Yes, the ring stores the spell energy and the various "ingredients" needed to release the spell energy, but it seems the scroll does also.  The spell energy has to be in the scroll because it doesn't require a spell slot.