At which point, what is Fuller House? Same cast (minus the Olsens) of the original.

A sequel series. Plain and simple. The new Frasier is this too.

It takes place some time after the original with mostly the same main characters, and they are the same characters from the original show.

No alternate universe, no alternate versions of characters, no retelling of stories, it’s just that time in the universe has jumped forward a few years.