Nightlightshipping is Espeon/Umbreon. It's a general 'ship. Now, if you went to go make "Wes' Espeon/Wes' Umbreon", you don't /need/ to, because the general 'ship already exists to cover all relating members...and /counts/.
Vineshipping is Ash's Bulbasaur/May's Bulbasaur. It's a specific 'ship. Now, if you wanted to go make Bulbasaur/Bulbasaur....well, you couldn't. Same species 'ships aren't allowed at all, unless they /are/ specific, such as Voltshipping (Surge and Kay's two Raichu) and Quilshipping (Dawn and Ash's two Cyndaquil).
Lagomorphshipping is Ash's Pikachu/Dawn's Bunneary. It's a specific 'ship. Now, /if/ you wanted to go make Pikachu/Bunneary...you /could/, but there's little point. I doubt many people are going to 'ship Pikachu/Bunneary outside the show's perspective, unless they wanna do some reversal romance bit, but...it's impractical.
Meaning: if you wanted to go make a Zoey's Leafeon/May's Glaceon, you cannot, because Elegantshipping exists to cover all instances. If you want to do May's Glaceon/Dawn's Ambipom, you cannot, because Acupunctureshipping exists to cover all instances. If you want to make a general, absolutely unrelated to the specific 'ship Pikachu/Piplup, you're welcome to it...but I advise against it.
I don't need people thinking that's the right name for the wrong couple.
Specific first -> general possible
General first =/= specific possible
Specific first = covers specific only -> general covers rest
General first = covers everything and more