– “De” is used to describe the way one main ingredient is prepared: un pâté, une confiture, un chutney, une terrine… all these are different ways of cooking one main ingredient. Note that the “de” here never becomes “du” nor “des”. It’s always “de” or “d'”: it means “of”.
ex: Une confiture de fraises, take away the fraises, you’re left with… sugar. It’s not much.
– On the contrary, “à” (au, aux, à l’, à la) is used to describe a flavor or a garnish: take away this ingredient, and you will still have something. It might not taste like much… but you will have something… You can replace the article by “avec” (with) and it should still make sense.
ex: Une tarte aux fraises: take away the fraises, you still have the tart, the cream…
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– a, an, one, some, any: the French indefinite and partitive articles.
– the: the French definite article.
You’ll find many expamples of articles used in context in my French audio books.