The practical difference is that many of the arguments against lab-leak theories in general are actually arguments against the gain-of-function theory in particular. Things like lack of markers that would indicate engineering, or the presence of markers that would indicate animal origins. So distinguishing the two candidate theories becomes important for discerning whether the evidence is for or against a lab leak: you can't use animal-origins evidence as evidence against a lab leak, only evidence against an engineered virus.
Intentionally seeking out potentially harmful natural pathogens from remote locations and placing them in close proximity to people isn't relevant to lab leaks? Then why are they studied under high levels of security in the first place?
GoF research is so obviously a bad idea. The risks are enormous and the rewards are minuscule. But lab leaks of natural viruses are indicative of problems too.
