HMRC Letters confirming earnings

[nafe12]

I've seen various posts mentioning letters from HMRC to confirm employment, earnings, etc.
Does anyone know what these documents are called?
As far as I can see - you can get
a) One for employment history (National Insurance)
b) One for all self assessment tax years

But is there any letter that covers all earnings/tax paid (including tax code adjustments that were not part of self assessment)?

[Casa]

Form SA302 for self assessment earnings/tax paid
https://www.gov.uk/sa302-tax-calculation

[nafe12]

Form SA302 for self assessment earnings/tax paid
https://www.gov.uk/sa302-tax-calculation

Thanks - though that says for self assessment. Though it was possible to pay tax on certain earnings without registering for self assessment - which is what I'd like a record of.

[Casa]

I assumed that was what you wanted as you wrote;
b) One for all self assessment tax years