>The term 'painkiller' is reserved for strong pain relief
Having claimed it was cultural. It have been helpful of you indicated which culture you felt this applied to.
In UK I'd say painkillers includes ibuprofen and paracetamol. I suppose with ibuprofen it's also referred to as an anti-inflammatory. Not sure how else one would refer to paracetamol other than with synonyms (analgesics) or euphemism (pain relief tablet).