Skim vs Scan. Subtleties, Not really synonyms?

Skim vs Scan. Subtleties, Not really synonyms?

I've looked up the words in a bunch of dictionaries and each one says
something different. As I understand they're kind of synonyms
I scanned the article for his name. - meaning I read it quickly to find a
his name?
I scanned the article - meaning there's no information about what I looked
for but still I looked for something particular such as a name, not just I
read it quickly ?
I skimmed the the article - meaning I just read it quickly?
I skimmed the article to find his name - The structure of the sentence
(mainly the prepositional phrase) comes into play and now it means the
same as the first example?
Am I wrong? They're just synonyms?