The dictionary classifies woollen as the adjective form and wool as the noun. However, the use of "wool blanket" is very widespread. Although "wool" is classed as a noun we often use nouns in this modifying / adjectival position.
It it the same with wood. We can equally say a wooden cabinet or wood cabinet.
I think the -en affix dates back to Anglo-Saxon times, but lots of nouns do not have a different adjectival form so you don't have this choice that wool and wood offer.
I had written this earlier but neglected to press "Post Reply" but I'll just chime in and say I basically agree. However, I think here in the US that woolen and wooden are falling off--which is a shame.
It's kind of like the difference between wood and wooden. There isn't much difference. I'd say wool is used far more often. Obviously one is a noun being used as an adjective while the other is an adjective only. The exception to the rule is that woolens (plural) refers to wool clothing, especially things like mittens, knit caps, socks, sweaters (cold weather gear).