Ports reuse the existing resources (graphics, sound etc), remakes have them made anew, such as in FF4 on PSP.
FF4 for GBA is a port, FF4 for PSP is a remake, even if it's still in 2D. Just like the Final Fantasy Origins versions of the first two games were remakes, not ports.
http://www.youtube.com/watch?v=udnqBcb2C0I
That is so much better that I doubt there is a single sprite shared between the original game and this version. The graphics and audio has been made anew - re-made if you want - therefore the game is a remake.
http://www.youtube.com/watch?v=h0Tj5DXd_bA
Same graphics as on SNES, slightly worse audio quality because the GBA doesn't have as good a sound chip as the SNES had. This is a port.