UV varnish is a thing--a varnish that is (nearly instantly) cured by UV light--but also, without any other qualifiers is going to suggest full-coverage coating ("flood").
While many people use the word varnish as a catch-all concept, as far as I know, UV coating is technically not a varnish, it is a curable liquid plastic. There are varnishes (clear inks), aqueous coatings (water-based), and UV coatings. Not everyone has equipment for UV coating.
Spot UV implies partial coverage, so it uses an extra plate or masked silkscreen on a separate printing pass and usually it is going to be a gloss "emboss" effect or it is applied to e.g. the images only. One might use this to have nice rich gloss color for photos on matte paper while keeping the paper texture in other areas.
It is not uncommon to do the UV coating on a separate pass from the process printing, but this depends entirely on the provider's equipment. Some providers will job it out to a different provider if they are not set up for UV curing.
It is also common to incorporate a Spot UV with an aqueous flood coating (or the reverse), which has a sort of resist effect (I think this is called strike-through varnish).
UV is usually glossier than Aqueous Gloss, but UV is a brittle plastic that cracks, so be careful about folds.