Hahaha, yes, I would agree with you that the coast guard, as well as special forces are highly effective versus those kinds of Pirates.
Though the Pirates in Pirates' Nest are not the ones that in Sumalia that have to fight to just survive (as it seems, as well as my limited knowledge about them). "Our" Pirates are more the ones that fight for freedom the way they see fit (no intervention anymore by a higher power -> Government).
You should see the Marines as the "army" of the Government. As the structure of the world in Pirates' Nest is more of an island-structure instead of a main-lands structure (WoW for example), having a division between land- and waterforces is not THAT reasonable (but I do agree that it is a possibility!), as most battles will be fought on the sea (at least the big battles). And as noted, if I understand you correctly with the following quote:
like in RL. marines cover more than just water, they fight in all fields.
You state that Marines do more than just fight on water, but also on land (In Pirates' Nest, also somewhat above the ground due to flying capabilities of some abilities), which would be the perfect fit of calling the army versus the pirates, Marines.
A very good question indeed! I hope this answered it?