I think your definition sounds like my definition of fusions vs crossovers! I've always thought of the key distinction as:

Fusion: characters from universe A have always lived in universe B (e.g. "what if Nick was a Jedi" - implying that he grew up in the Star Wars universe and hasn't ever been his canon Toronto police officer self)

Crossover: characters from universe A meet characters from universe B (e.g. "what if Duncan & co. met Han Solo and traveled on the Millennium Falcon") but both sets of characters are still their usual canon selves with their usual backstories, aside from whatever is required to get them to meet - a portal or magic or time travel or whatever.