Are these terms used interchangeably or do they have to be specific?

For example, Shaggydog has a benefit that occurs when a Lord is under your control. Does this also work when Catelyn Stark is in play? The confusion stems from the fact there is an icon (the crown) for Lord that both Lord's and Lady's have.

I dont know what you mean by there being an icon called the crown but regardless Lord and Lady are NOT interchangeable.

Cards will specifically refer to a Lord or Lady in play

Daenarys said:

I think OP is referring to either the power challenge icon, or the [ring] that denotes a noble character.

As Daenarys said, Lord and Lady are traits. These are not interchangeable, they don't mean the same thing, and anything that is dependent on one of those traits will have it on the card in bold italics as I have demonstrated here.

Yes it's the ring icon, I thought that meant Lord/Lady since it's always on those cards.

You will find details about the war, noble crest etc near to the front of the rule book.

On their own they do nothing but you will find cards will reference them .

Note that you can find Lord and Lady characters without the Noble crest in the Core Set (Bran and Arya Stark) and many more in the other packs. Characters with the Noble crest but without the Lord or Lady trait are rarer, but exist as well: Baelor Blacktyde, Bastard in Hiding, The Sparr.