So when is a remake indeed a remake?
When it includes the same basic elements.
Total Recall. A guy living a mundane, boring life dreams of a more exciting one. He learns about Rekall. He goes to Rekall and checks it out. He sees that through some amazing miracle, they have the
exact scenario he's been dreaming about lately and decides to go through with it. One of the elements he includes to make it even more spicy is that of a superspy. The memory is implanted...
...and suddenly, he's thrown into a Machiavellian scenario that includes every single element he ordered. He discovers he's an undercover plant trying to thwart a rebellious force. During the scenario he also discovers that the side he's working against is actually the side he's working
for, but he rebels and joins the side he was supposed to be infiltrating. He soon discovers that some grandiose secret is being kept from the general public that could have a massive effect on all of humanity; most likely something to do with aliens, but not necessarily.
Throughout the entire scenario, he keeps running into people who shouldn't be there, each one claiming to be an implanted memory from Rekall trying to help him out. But due to his own paranoia and the parameters he selected for the scenario, he finds some random element that causes him not to believe them.
As the story concludes, he uncovers the huge conspiracy, reveals it to the world, and gets it on with the dream girl he chose when he sat down in the chair at Rekall.
Notice the lack of any mention of Mars, three-titted chicks, mutants, or psychic powers? That's because they don't matter to the story.