Polymer nomenclature tends to be confusing at times, largely I think of it being created faster than it can be standardized. Polyvinyl alcohol is my favorite misnomer, as it implies that the polymer is made from the polymerization vinyl alcohol . But another one that is almost as bad is the whole polyethylene glycol/polyethylene oxide dichotomy. If you are not aware of it, let me illustrate.
Here is the structure of polyethylene glycol (PEG):
and here is the structure of polyethylene oxide (PEO):
If the difference isn't apparent to you, don't worry, there isn't one. The only difference between the PEG and PEO is molecular weight, which is set at the totally arbitrary limit of 20,000 Daltons. Below that limit, you have PEG. Above that limit you have PEO .
Why the limit? I'd love to know. Somebody at some point in the past made the decision for the difference  and we are stuck with this duality for all eternity.
 Vinyl alcohol doesn't exist. It undergoes a keto-enol isomerization to form acetaldehyde. The polymer is actually made from the hydrolysis of vinyl acetate, replacing the acetate side chains with hydroxyl groups.
 What if you are at 20,000 exactly? Then what?
 I'll give to 100-to-1 odds that it was a marketer.