This was a great question and I appreciate your time in explaining. I too am having this issue where after El Capitan install I found I have a "new" IMAP account in mail....I'm not exactly sure how that happened. I have the same question about POP vs. IMAP. Based on what you have commented, how is an IMAP acct. different from a POP acct. IF with a POP acct. I never delete emails that have just been downloaded to my "device"...they just always stay on the server until I am notified that I need to free up space....about once every two years I need to manually delete tens of thousands of emails 😟 If they always stay on the server it doesn't matter which device I access them from...or....which one first.
Am I still missing something?