> The law doesn't care about your intent.

This isn't correct. The law in most modern democracies, as far as I'm aware, is very concerned with intent.

This why we generally define murder and manslaughter as distinct.

Murder is the unlawful killing of another human without justification or valid excuse, especially the unlawful killing of another human with malice aforethought.

https://en.wikipedia.org/wiki/Murder

Manslaughter is a common law legal term for homicide considered by law as less culpable than murder

https://en.wikipedia.org/wiki/Manslaughter

Murder vs manslaughter is the extreme example, though you'll find courts are broadly quite concerned with intent.