In an altered reality Magneto began a mutant movement which caused mutants to be the majority on the planet and normal humans to be the minority.

The House of M reality is simply a name for the unique state of existence created by the Scarlet Witch. It is indeed an ALTERED reality--not an ALTERNATE reality. It was so altered that events that occurred in the history of Earth-616-normal did not necessarily affect those in the House of M reality, nor vice-versa. Reality-58163 is a core continuum designation for this unique altered reality and the events that occurred within that altered reality.