HR contacted me with an approved offer.

On the portal, the position advertised is "director"

Based on the experience, I am overqualified. Based on the title, I am under qualified (now a manager) but I am sure I did well in the interview and my new boss likes me. Exceeded his expectation. I know I am behind my peers by at least 2k and 1 rank.

Current Salary = $9. Title=manager
Initial offer: Salary = $10. Title=director. Dx 12
Approved : Salary = $12. Title=Senior Mgr. Dx 11

What happened? Is anybody able to advise?

All is just an example, I just want to indicate that salary increased, the rest dropped.

I agree that that salary is king, I concur but I hope to know what's going on. The rank somewhat matters. if one day I go back to corporate, many invite you to the interview based on perceived rank too.

Should I press for the higher dx rank, will I lose out when it comes to ranking, PB etc?

Tq