Is There A Technical Definition For A "Limited Edition Proof Set" Compared To A Regular Proof Set?

There are at least three levels of US Mint Proof Set:

1) Standard: Contains base metal composition circulation coins - cent through dollar.
2) Silver: Contains fine silver versions of the dime, quarter (all Types) and half dollar (other included coins are struck in their standard composition).
3) Limited Edition: Contains fine silver versions of the dime, quarter (all Types) and half dollar PLUS an American Silver Eagle (in 2021, two ASEs were included - one of each Type).

The Standard Proof Set does not have a mintage limit - it is made to fill orders recrived (though the Mint might announce a cutoff date late in the year).

The Silver Proof Set does not typically have a mintage limit - it is also made to fill orders received (with the same caveat as above).

The Limited Edition Proof Set does have a mintage limit, historically set at 50,000.

The Mint also produces single-denomination Proof Sets (Statehood Quarters, American Innovation $1, etc.) in addition to the multi-denomination sets. Some of these sets are struck in silver as a premium version of the standard release.

Technically, any time a mint assigns a maximum mintage for a mint product before they actually start making them, that product is a "limited edition" and can legitimately be marketed as such. Most non-US-government mints make large amounts of such "limited-edition" NCLT and have been doing so for decades, so the US Mint is really just jumping on the same old bandwagon here.

Of course, you have only the mint's word that the "limited edition" will in fact be limited as advertised. But if a mint happens to stumble upon a record-breaking best-seller where demand far exceeds the anticipated supply, they might be tempted to extend, expand or re-issue a "limited edition" coin. Most mints would be expected to resist that temptation and keep their word, lest their reputation suffer, but if a mint's reputation is already in the trash heap, they're not going to care and "limited edition" simply becomes marketing jargon devoid of any actual meaning.

One thing to note about the LESPS is that you can get all the constituent coins from other US Mint products at retail generally for cheaper than you can by buying the LESPS. The only thing that really is "limited" about the LESPS is the packaging which, as commems mentioned, has historically been set at 50k.