Confused about tax and social security numbers (Munich)

Hi all,

I hope someone here can help me out as I am getting confused by conflicting information on official sites.
I recently arrived in Germany as I will be starting employment here beginning of June, and am going through all the steps of registering and getting set-up here.

I have registered at the KVR and was told I would receive my tax number (steueridentifikationummer) automatically.
Other sources say I should apply for it separately at the Munchner Finanzamt or yet again another said I would receive it automatically once I start getting my salary/ file a tax return.
Does anyone know which is the case?

And who issues a social security number (sozialversicherungsnummer)?
On one site it says the employer registers the employee at a pension scheme and a social security number is generated through that, on another it seems I have to apply for it myself, somewhere...

Grateful for any help!
Jo