They can mean practically the same thing in certain contexts. But they have nuanced semantic differences that can be a big deal in some scenarios.

They are not the same. The first is quite casual, and the second is casual too. The word "cozy" could have a friendly, familial, or romantic connotation. "Intimate" is probably romantic here. This partially because to be "intimate with" someone often means something specific and very, very intimate, if you catch my meaning. The more context you give us, the more helpful we can be with your question. Whether these all mean the same thing or not depends on the context.