There's a difference actually.
A port is when you take a game from one system, and stick it on a different system. A few tweaks might be done here or there to get it to work, but for all intents and purposes, it's the same game. Zelda OoT would be an example of an enhanced port. It's a port in the same way Perfect dark on the xbox is an enhanced port.
A Remake is a game made from scratch, the ground up, based on an existing game. Resi 1 on gamecube is a good example. MGS Twin Snakes is another. Only difference is, it's using the MGS2 gameplay engine, and thus breaking the game in many ways (the difficulty mainly) since the game wasn't designed for a lot of the features that were added in MGS2.
Anyway, the "art style" is pretty much the same, but the game ran no where near as well as MGS2 did, slow down etc is to blame in this case.