No difference.
Despite being an old question, I'll have to put here the other perspective. According to JC,
- So the durations "Until Dispelled" and "Permanent" are functionally equivalent unless we houserule one of them?
- That's correct.
And according to Sage Advice,
- Can permanent magical effects be dispelled? Or are they
no longer considered magical effects once permanent?
- If
the effect of a spell becomes permanent, it can be dispelled,
unless its description says otherwise (such as in the wall of
stone spell).
Some spells do say "until dispelled", like Forbidance or True Polymorph, while others use the "permanent" nomenclature, like Private Sanctum. The discrepancy is strange, but it may have been an oversight from the designers. I think the idea is that, any magical effect created by a spell can be dispelled, thus falling in line with Dispel Magic's text.
Choose any creature, object, or magical effect within range. Any spell [...] on the target ends.
There are no assumptions regarding the duration of the effect, only that its spell (and thus effect) is terminated. Also consider spells like Wall of Stone, that claim
If you maintain your concentration on this spell for its whole duration, the wall becomes permanent and can’t be dispelled.
So, despite being permanent, they specify how they can't be dispelled. This seems another indication that permanent just means "infinite duration".
As a DM, maybe you can house-rule it so that it is much harder (or even impossible) to dispel permanent effects (similar to Artifact magical items), but at least according to the designers, it seems that, as you asked, there is no difference between "until dispelled" and "permanent".