Ghostbusters was rebooted with Ghostbusters: Answer the Call. It ignored what had come before, and told a new (but similar) story with new characters.
Here’s a page about reboots on Wikipedia.
A reboot tends to toss out what has come before, and tell a new story with (sometimes) new characters, and is easy for new audiences to grasp without knowledge of the original. With Ghostbusters: Answer the Call, it had a new villain with a unique way of bringing ghosts into our world, and the characters are distinct from the characters in the original films. The same is going to be true of the upcoming Ocean’s Eight, which is a reboot of Ocean’s Eleven, which is a remake of Ocean’s 11.
The Karate Kid was remade with The Karate Kid… sigh… this was pretty much a scene for scene copy of the superior original film. According to reports from those who made the sacrifice to actually view this film (hope they got paid to do so), if they wanted to watch The Karate Kid again, they would just pop in the original.
This has been happening for a very very long time. List of film remakes.
A remake is pretty much the same work, with a new cast, telling the same stories as before. In the case of Karate Kid, they changed some of the story, but not enough for it to be considered a reboot.
Star Wars: The Force Awakens was a direct sequel to Star Wars: Return of the Jedi. Though it was released 32 years later, it continued the story and characters.
Rogue One: A Star Wars Story was a direct prequel to Star Wars: A New Hope.
What does this mean for The Matrix reboot? We’ll see if that’s what it is when we know more about the direction that it is taking. We don’t know anything about it yet. It could be a remake… it could be a reboot… it could be a sequel… it could be a prequel. Fact is… we won’t know until something leaks or someone speaks about it that knows the facts.