Most hosting companies and providers offer both options. If you’ve been using a POP account, but have grown frustrated with inaccessible messages, you can usually convert your account to IMAP. With IMAP, they’ll be on all your devices. For example, with a POP account, if you check email on your iPhone, the messages downloaded there will only be there when you get back to your Mac, you won’t see them in your inbox.
Or, you can have an IMAP (Internet Message Access Protocol) account that leaves some or all of your messages up on the mail server so you can access them from any device. You can have a POP (Post Office Protocol) account that downloads all your messages to your Mac, iPhone or iPad. Most email providers let you choose between two ways to get your messages.