Developmental editing (or substantive editing), as the name implies, involves checking the content.
Per the Chicago Manual of Style, developmental editing more directly shapes the content of a work, the way material should be presented, the need for more or less documentation and how it should be handled, and so on. Since developmental editing may involve total rewriting or reorganization of a work, it should be done—if needed—before manuscript editing begins.
Copy editing is checking a copy for spelling, capitalization, punctuation, verb tenses, and other grammatical errors.
Per the Chicago Manual of Style, copy editing (or line editing) requires attention to every word and mark of punctuation in a manuscript, a thorough knowledge of the style to be followed, and the ability to make quick, logical, and defensible decisions. It is undertaken by the publisher—either in-house or through the services of a freelance editor—when a manuscript has been accepted for publication.