All 0W20s are synthetic but not all 5W20s are.
I think Pennzoil and Motorcraft have a 0w20 syn blend.
Shouldn't respond before checking things out but....
Lots of syn-blend oils (5w-20 and 5w30 still market themselves as conventional because they have "syn-blend" brands marketing themselves at a higher price point.
Could these "syn blends" be all synthetic (i.e. group 3) and marketing themselves as syn blends because there's a "synthetic" at a higher price point?
It will be interesting to see how this all shakes out when SP oils hit. Lots of branding confusion ahead.