Spells and spell schools.

Alright so while familiar with DnD I'm not all knowing and have a few questions about spells and spell schools. I've been looking at some other sites about the DnD spells and then at the ones we have in Baldur's Gate, and wondering which is wrong and if it has anything to do with editions.

Baldur's Gate :

Power Word Blind - Conjuration
Power Word Stun - Conjuration
Power Word Silence - Conjuration
Power Word Sleep - Conjuration
Power Word Kill - Conjuration

Symbol Death - Conjuration
Symbol Fear - Conjuration
Symbol Stun - Conjuration

Flame Arrow - Conjuration

DnD sites :

Power Word Blind - Enchantment
Power Word Stun - Enchantment
Power Word Silence - Enchantment
Power Word Sleep - Enchantment
Power Word Kill - Enchantment

Symbol Death - Necromancy
Symbol Fear - Necromancy
Symbol Stun - Enchantment

Flame Arrow - Transmutation

I'm sure there are other spells too that will be different, so i'm curious here, who is right? I've been looking at mage specializations and some (Conjuration) seem to have a lot of spells that don't really belong there in my opinion.