It all depends on the group they belong to and that is determined by their content. PAO's which compromise group IV and V are synthetics, group III have a highly refined base with synthetic additives.
There is a marked difference in the meaning of synthetic and synthesize., No semantics can change that, only incorrect usage in content.
Group II and III oils are refined not synthesized, there is a marked difference there also. Claiming a group II engine oil is synthesized is factually wrong, it is refined petroleum period. Claiming a group III base stock is synthesized is technically incorrect also. It is simply refined beyond what can occur in nature, and then the marketing fights began.