morir vs matar
Morir is to die. Matar is to kill. The reflexive forms morirse and matarse change the tone completely.
morir / morirse
To die. Morirse is more colloquial and used for figurative death.
Murió en 2010.
He died in 2010.
Formal and written. Stem change o→ue: muero, mueres.
Se murió mi abuelo.
My grandfather has died.
Morirse is the usual word in speech for a death in the family.
Me muero de hambre.
I'm starving.
Figurative: morirse de hambre/risa/frío/sueño.
matar / matarse
To kill, or to kill oneself accidentally or figuratively.
Mataron al rey.
They killed the king.
Deliberate killing.
Se mató en un accidente.
He was killed in an accident.
Matarse = to die by accident, or to kill oneself, context decides.
Me mata el calor.
The heat is killing me.
Figurative. Also 'matar el tiempo' = to kill time.
Tricky bit
'Está muerto' = he's dead (state). 'Lo mataron' = they killed him. 'Murió' alone doesn't say anyone caused it. In news, 'murió' vs 'fue asesinado' matters.