Sure there is a difference, it's not just two names for the same thing! However, POP is a different way of getting mail, the process of sending via SMTP server is the same.
This may solve your problem and get you onto IMAP (which is the better way anyway - use Google to find out why):
1. Don't leave out any of the following steps or mess up the order, otherwise you might lose mails!
2. Backup, if you haven't yet.
3. Have you backed up? Really?
4. Add a new email account as IMAP with the same, correct access data. All your mail will then always keep residing on the server (as opposed to POP where incoming mail gets eventually deleted once you've downloaded it).
5. Are you getting mail through that account? Can you send mail? If so, continue. If not, delete the account, stop this sequence here and let us know. Also, consider contacting your ISP's support.
6. Which mails are you getting in the new inbox (and in "sent"), only new ones, or also old ones... possibly all old ones?
7.a. If only new ones: Drag and drop all mail from your POP mail boxes and folders to the equivalent boxes and folders of the new IMAP account. This may take a while, depending on how many mails and attachments you have as it's all uploading to the server.
7.b. If few older ones: Drag and drop all other, even older mail from your POP mail boxes and folders to the equivalent boxes and folders of the new IMAP account. This may take a while, depending on how many mails and attachments you have as it's all uploading to the server.
7.c. If all older mails, both inbox and sent: Nothing to do, on to the next step.
8. Delete the old POP mail account. Don't do before having successfully moved all mails to the server! Deleting the mail account will delete all its mails as well! Just in case, you have a backup, yes?!