Normal Order Reduction (NOR) reduce the leftmost, outermost redex.
Normal Order Evaluation (NOE) reduce the leftmost, outermost redex, but not within the body of abstractions.
So (λw. (λx.x) z) is in normal form under NOE, but not under NOR.
Does using NOE instead of NOR weaken the Normalization property?
The Normalization property states that if there is a normal form under beta-reduction, that NOR will find it. Edit: Sorry, it's the Curry/Feys Theorem that says that NOR always finds a normal form if it exists.