で and と particle can be used to mean "and" in english. For example:
In the sentences above, both と and で means "and", but they are not interchangeable. When would one use と and で to imply "and" in english?
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In Japanese you can chain independent statements together by conjugating the statement in the middle into the te-form and just sticking them together. This is what's happening in your first sentence, with で being the te-form of だ. There are two complete statements there: お金持ちだ and きれい. Those both work as sentences by themselves.
The と particle is used for grouping nouns together. (It has other uses as well that aren't relevant here.)
A noun by itself isn't a complete sentence, nor can it be conjugated, so the first method doesn't work on the second sentence. And likewise, since the first sentence isn't combining nouns, と doesn't work there.