was not aware和doesn't realize有什么分别?

aware是adj.
realize是verb

aware例句:she became aware that something was burning.~她發覺有東西燒著了
realize例句:she realized that he had been lying.~她明白了他一直在說謊

'She was not aware' tends to be used after the event, so someone wasn't aware that they weren't supposed to leave the oven on a high temperature.

'She doesn't realise' would be used in the present, so used in something like oh my god she doesn't realise that her rabbit has died.