You most likely have your email account set up on your phone as a POP3 account. This means that it is not synchronising with your laptop.
When it is a POP3 account it will register that you have an email but because you are deleting it from your laptop when your phone tries to download it the email is no longer on the BT servers because you have already deleted it using your laptop.
If you want your laptop and phone to synchronise you will need to set your phone's account up as an IMAP account. This will mean that everything you do on either your phone or your laptop will be replicated so if you delete and email on either of the devices it will be deleted from the other device and if you send an email on your laptop you will be able to see the sent email in your sent box on your phone and visa versa.
See link for further information.
What are IMAP and POP? - Microsoft Support
