"Distinguish" and "differentiate" are both good here. They both match the tone of the sentence well, but have slightly different meanings. "Discern" also works well.
"Tell" is okay too, but is a less classy, more childish way of speaking, since it's a much simpler and more common word that's also more vague, carrying multiple meanings. So it doesn't match the tone so nicely. But if you remove the word "that" and adjust the ending a bit, as in "she said she could tell what wine it is by smelling it" then "tell" matches this basic tone perfectly.
Discriminate is not a word people tend to use for sentences like this. It usually carries a negative connotation. When people think of discrimination, they usually think of racism and similar "hate crimes". This may have been different a few decades ago - the world has gone a bit mad with political correctness lately. Having said that, it can still technically work today, it's just not such a natural usage. If you really want to use it, I would recommend assisting it by adding the word "between". For example: "She said that she could discriminate between different types of wine by smelling them". Adding "between" like this, also improves the clarity of the sentence when using any of the other word options, but it's less necessary in those cases.