When a pokemon keeps going away for a trade and then back again, it's most likely a person cloning that pokemon.
It's actually not a glitch when a pokemon named Ponyta shows up as Seaking, and vice versa. You can deliberatly nickname your pokemon so that happens. So if your Seaking is nicknamed Ponyta, it'l show up under a Ponyta search.
I still don't know if that same Seaking would appear in a Seaking search, though. Oh, and...
SEAKING - **** YEAH!