From the IFAB VAR protocol:
"The referee can initiate a ‘review’ for a potential ‘clear and obvious error’ or ‘serious missed incident’ when:
- the VAR (or another match official) recommends a ‘review’
- the referee suspects that something serious has been ‘missed’"
And
"For subjective decisions, e.g. intensity of a foul challenge, interference at offside, handball considerations, an ‘on-field review’ (OFR) is appropriate"
This is the only published protocol. PGMOL have their own protocol which may amend the above for one reason or another (probably "another"), but that isn't published afaik.