By contrast, comfort has a more general meaning, though it could be used in place of console. Comfort does not always have to be applied to pain and hurt that is very deep, as would be the case with "console".
As well, "comfort" is often applied to that which is concrete or physical. It's possible to comfort someone while they're sick by making them tea and bringing them soup, for example. However, one would not use "console" in such a way as this. We typically reserve console for more abstract notions of helping someone to feel better or get through a difficult time.
[I would recommend using monolingual English dictionaries. Sometimes when using a bilingual dictionary, it's hard to notice differences in words that have similar meanings or are sometimes synonymous.]
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