> Also, how come we always only count murder, as opposed to gun violence?
Because other countries use different definitions for those things. The definition of a "firearm death" is consistent, someone was shot they're now deceased.
The definition of "gun violence" could be a gun that wasn't even loaded or fired in some countries (e.g. pointing it menacingly), bullet-injury in others, pistol-whipping in yet others, for one example.
Crime statistics are a complex topic, with politics, collection methods, and definitions playing a major part. For one example, richer countries often have higher "crime" because they're better at collecting and recording crime statistics, not because crime doesn't occur in poorer countries. Even richer countries like the US have a "crime gap" if you compare recorded crime with victim crime surveys (e.g. NCVS).