Z-spread vs OAS additional, confusion, account, example, forward

dvilayphet

It is my understanding that OAS takes into account liquidity and credit risk. Z-spread adds option premium to OAS.

Here is my confusion:

If you are valuing a bond with embedded options (e.g. callable bond), you add same OAS to forward rates to find an arbitrage-free present value. Why are we callin this additional spread OAS and not Z-spread?

Second Confusion:

Similarly, I am somewhat confused where we do spread analysis for Fixed Income securities. For example, when looking at Mortgage Back Securities (with prepayment option), why are we using OAS and not Z-spread?

Thank you for your comments.