This is the plant and the fruit, not the drink. The grape is green-skinned, and it is grown for wine rather than for eating. What makes it unusual is how easily it settles in: it will grow in cool places and warm ones, so farmers in very different countries can all plant it. When you mean the fruit and not the wine, the clearest thing to do is add the word grapes or vines after the name.

The wine carries the name of the grape it is made from, which is how many wines are named in English. Because the grape grows almost everywhere, Chardonnay is not one fixed taste; where it was grown and how it was made change it a great deal, so people usually say which country or which maker they mean. In a sentence it behaves in two ways. As a drink in general it is uncountable — a glass of Chardonnay. As a type or a named bottle it can be counted — a good Chardonnay, three Chardonnays from the same valley.