In other words, we have a Highborn, rich, upper class, land owning Lord.
We also have a poor, lower class, landless Lowborn.
In conversation, the Lowborn addresses the Lord through, "My Lord."
The Lord tells the Lowborn to address Lords with, "Milord," due to their lower class. Whereas if a Lord was speaking to another Lord, they would use, "My Lord," since both Lords are upper class.
Was this an actual social courtesy during medieval times?
Were phrase distinctions like these common then? What other phrases were specific to certain classes?
First of all, minor spoilers for season 2!
I assume you're referring to Lord Tywin speaking with Arya Stark. When he tells her that she should be saying 'milord' rather than 'my lord' it's because he realises that she is a highborn girl who is pretending to be a commoner. Pretty much he's telling her that if she wants people to believe she is an uneducated common girl then she should speak like one. Nothing to do with a correct way to address a Lord, just that she should hide her posh accent better.