E-Mail on iPad and E-Mail on Computer not connected
Hotmail uses the POP protocol. This protocol only allows to download mails from the server. Therefore it does not sync mail for example to mark them as read. 

If you want to fix this you have to configure your Hotmail account to uses the IMAP protocol which allows the synchronising... But this is really tricky to do.  : 


If it's not done : Migrate your Hotmail account to Outlook.com
On the iDevice : Settings > Mail, Contacts, Calendar > Other
Add Mail account 
Add a fake mail account (if iOS detecte a @hotmail.com, @live.com or @outlook.com it will suppose it is POP only) 
You'll get an error (normal, you added a fake account) 
After this you'll have 2 tabs : IMAP and POP, file the IMAP tab with the following infos : 

Incoming mail server :

Host Name : imap-mail.outlook.com
Port : 993
SSL : yes

Serveur sortant :

Host name : smtp-mail.outlook.com
Port : 587
TLS : yes