These phrases are similar but not the same. Copy-cat means a person who doesn't have ideas of their own and does or says the same as someone else. Cookie-cutter means to lack originality; to look the same to other things of the same type. Cookie-cutter is more commonly used towards an object, such as houses or clothing.
Ex: They live in a cookie-cutter home. It looks exactly the same as the rest of the houses on the street.
Ex: She is such a copy-cat. Always doing everything that he does.
Ex: That store is very cookie-cutter. They don't have anything unique.
Ex: I used to be a copy-cat of my sister until I found my own interests.