I'd distinguish popular usage and etymology. Terrorism is about terror. Mass murder is about a lot of murder. Mass murder can be not terroristic (a lot of people murdered, but population not terrified); terrorism can be not mass murderous (mass murder isn't the only way to instill terror); and, violence for a political purpose isn't always terrifying (or mass murderous, for the sake of completeness).
> Mass murder can be not terroristic (a lot of people murdered, but population not terrified)
I think that would be such a rare scenario as to be worthless as a premise. Can you name a bunch of prominent examples where a lot of people were murdered, and it didn't generate terror in the population nearby the event (or broader, perhaps nationally, if it was at a genocidal scale)?
I can think of few examples from recent history.
Serial killers inspire terror in the population in the region where the killings occur.
Mass shootings cause terror.
Authoritarians/tyrants, civil wars and other military conflicts that genocide populations cause terror.
When is there ever a lot of murder without terror? The only cases I can think of that didn't have terror immediately associated, are the rare instances where the population didn't know until afterward, and even then it's likely there would be some terror felt after the fact. For example, nurses that get caught having committed mass murder (several prominent examples from the last ~40-50 years). Often they don't terrorize a population while they're committing murder, because it's unknown what they're doing, however it's also very likely the population feels some terror afterward in the form of lingering fear and loss of trust & security in the healthcare system. In that example, the infliction of terror merely occurs with a delay.
An example I have in mind is gang related murders in US (e.g. Chiraq). Their scale is greater than all terrorist events in US put together, yet the media/popular reaction to it is orders of magnitude less. It might not be obvious to everyone, but we're quite picky as to when to get terrified.
Mass murder/serial killings aren't terrorism because their intention is not (necessarily) to inspire terror. Serial killers especially tend not to care what the populace thinks of their actions; they do it for very personal reasons. That's not terrorism.
