Or Y E't.

The first list of 8 all seem to have, as part of their pronunciation, phonetically, a letter of the alphabet (although Kale might depend on some regional accent). But that only makes one category.

Perhaps the differentiation is that in some cases the letter name sound gets its own syllable, and in other cases there's a consonant at the end tacked on to that syllable.

Syllable by itself: Cucumber, Peanuts, Seafood.

Sharing: Beets, Cake, Kale, Veal, Wine.

"Why" is in the first category. "Eat" is in the second.

Another categorization might be whether or not the word has the letter in its spelling that it has in its pronunciation:

Beets has a B.

Cake has a K.

Cucumber does not have a Q.

Kale has a K.

Peanuts has a P.

Seafood does not have a C.

Veal has a V.

Wine does not have a Y.

A variation could be a requirement that in order to count as actually having the letter, to require that it have it at the beginning. This would switch Cake to the "lacking" category.

French Fries is a borderline case, but it shows that either of the above categories requires that the letter sound be either at the beginning of a syllable or be the entire syllable. With its I sound in the middle of a syllable, between fr and s, it doesn't come at the syllable's beginning.