No, the difference is that IMAP doesn't store anything other than headers on the client (at least, not until the user tries to read a message), while POP3 eagerly downloads messages whenever they're available. A POP3 client can be configured with various remote retention policies, or even to never delete downloaded messages.

I don't have an IMAP account available to check, but AFAIK, you should not have locally the content of any message you've never read before. The whole point of IMAP is that it doesn't download messages, but instead acts like a window into the server.