I don’t think it’s a different sense of the term. It’s extremely common in mathematics and science to refer to some variant of an entity—say, x—as x′ (“x prime”). A second variant would be x″ (“x double prime”), and a third as x‴ (“x triple prime”). Given that Star Trek is in a science fiction setting, I think this mathematical terminology is exactly what this “Spock prime” designation is aping.