Everyone tries to distinguish these two, it's mostly just in the eye of the beholder - IMO aggression is just assertion when it's judged to be inappropriate or incompetently done - a drill instructor being assertive looks different to a police officer in a stand-off which is different to how you talk to co-workers - the distinction is highly contextual and subjective.
I think a lot of people with poor social skills thinks the aggression / assertion line is all about being angry or shouty or rude. Assertion uses a bunch of tools (including potentially - a louder or quieter voice, appearing angry, threats, manipulations, etc) to achieve a goal. Doing so in an inappropriate way is seen as aggressive (e.g. threatening to quit over a minor issue). Overusing any given tool (e.g. swearing a lot instead of realising a different tool is needed) is seen as incompetent (or losing control) thus it's seen as aggressive. But fundamentally there's no real objective difference.