A terrorist is not simply someone who creates fear amongst the public. If that were the case every single news outlet would technically be a terrorist organisation.
If this man killed her for political reasons, then he killed her because he believed the act would cast fear and terror within politics, and is therefore a terrorist. A terrorist doesn't have to have something against the public for him to be a terrorist, where did you get that idea? No, his aim is not to cast terror to the public, it's to cast terror to politicians, IF of course it was politically motivated and not just a random slaughtering.
In fact the definition of terrorist is "a person who uses terrorism in the pursuit of political aims.". It's got nothing to do with casting fear amongst the general public, that's the job of news outlets.
In fact you say "More and more this looks like an individual that was specifically targeted." but you conveniently forget the fact that this "specific" woman was a politician? Cognitive dissonance?