A remake takes the original source material and copies it directly. A sequel is a continuation of the original source material. A prequel is a story that takes place before the original source material and ties into it. A reboot is a re-imagining of the original source material and draws inspiration from it.
"Dark Knight" is a sequel to the alternate story line of the comics collectively known by the same name. I should have have listed it as an 'alternate story line sequel', you are correct.
"Rise of The Planet of The Apes" is a story that takes place before the original story of "Planet of The Apes" and ties into it by explaining how the apes came to possess advanced intelligence.
"Star Trek" takes place before either the series or "Star Trek: The Motion Picture", but it also explores an alternate time line.
If you want to lump all sequels, prequels, reboots, and remakes into the same category, that's fine. I thought that we were focusing specifically on movies that simply redo what has already been done without adding anything to them.
Yep, we must've been typing at the same time. I take it back -- reboots and remakes are definitely very different from each other.
On a side-note, "Apes" is definitely a reboot, not a prequel. Ditto for "Trek". If you're familiar enough with the franchises, it is clear that they took it in a very different direction; different stories, completely.
Whatever, you're right -- reboots, remakes, etc., should not all be lumped into one category.
How about "Dawn of the Dead"? That's pretty awesome, and it's definitely a remake!