If you're account uses POP3, then one device is likely set to delete emails when they are downloaded, and the other not. It sounds like your iPhone is set to delete from the server.
You can confirm this by going into the advanced setting in the iPhones and looking. I can't show you exactly where, because I don't have a POP account.
If it is on, then anything you view/download first on the iPhone will be deleted from the server, and not available for download on the iPad. If the iPad is set to leave the mail on the server (which is the default setting) what you do on it will not have any affect on the iPhone.
Setting it not to delete on either device will leave your email on the server (until it fills up) unless you go in with some other device/computer and delete it there.
Complicated?
Frankly, unless you know exactly what is going on, POP is a pain to use with mobile devices. Most people who have POP accounts leave their mobile devices set to not delete off the server, then do all their clean up on a desktop client.
I'd check with your email provider and see if they have IMAP or Exchange setup options. If they do, set everything to those servers and everything will stay in sync; because all changes are made and synced on/with the server, not on the devices.