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.
You have no idea how long that debate has been raging in my lab. On expert says PEO one say PEG its fun as long as I get my product.
A better distinction between PEG and PEO may be in the ways they are synthesized. The repeating unit of polyethylene glycol, by name, is "ethylene glycol" which does not exist, implying that PEG is and can only be synthesized by hydrolysis of another polymer. On the other hand, the repeating unit of polyethylene oxide is "ethylene oxide", and this time it mean literally that PEO is synthesized by polymerization of EO.
Ethylene glycol certainly does exist - the Wikipedia article and is used as a comonomer to make PET.
I certainly wouldn't try to make PEG by polymerizing it however, as there would too much water coming out all over the place. As you noted, polymerization of EO is the preferred option.
I certainly agree with Andrew Sun. The difference in naming PEG and PEO is because of their different synthesis route to the final product. I have never heard of the 20,000 limits. As Sigma-Aldrich page indicates that PEO of Mn=10,000 is still called PEO (http://www.sigmaaldrich.com/catalog/ProductDetail.do?lang=en&N4=44101|FLUKA&N5=SEARCH_CONCAT_PNO|BRAND_KEY&F=SPEC) and PEG that has Mn 35,000 does not lose its name into PEO (http://www.sigmaaldrich.com/catalog/ProductDetail.do?lang=en&N4=81310|ALDRICH&N5=SEARCH_CONCAT_PNO|BRAND_KEY&F=SPEC)
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