"Co-founder" is a fuzzy title that means exactly what the people in actual positions of authority want it to mean. But usually its an explicit up-front agreement at the time a person is brought on, or one made with a real status change later (even though an after the fact "co-founder" seems at odds with the common understanding of the term.) The firm might want to grant the person the title of "co-founder" if they feel the past and ongoing contribution warrants it (and, particularly, if the value of keeping them happy is high.)

"Partner" is a legal relationship; you can only be a partner in a firm which is a partnership (not a corporation).

Otherwise, the person is just an employee.