Being assertive and aggressive are not variations on the same thing. In fact if you observe people with actual power they tend to rely less and less on aggressive behavior, and more on suggestions and persuasion.

I think it would be a mistake to characterize assertiveness as just a subset of aggression, defined as all aggressive acts less the inappropriate ones, or the reverse, as you seem to be arguing here. I think it's more accurate to say there's a very small set of cases where they overlap.