Some people call MSN Messenger Hotmail Messenger because most of people are using their Hotmail email addresses as MSN login. This is because of the fact that Microsoft is the owner of both MSN Messenger and Hotmail email service.
It is not necessary to use Hotmail address with MSN Messenger, you can use any other email address, for example Gmail or any other. Then you can't call it Hotmail messenger :)
Conclusion - what you are calling the Hotmail Messenger it is actually only MSN Messenger (or Windows Live Messenger) and it is wrong to call it HotMail Messenger because you don't have to use Hotmail for your messenger login.