A borrowers' credit history is very important when it comes to mortgage lending. Credit scores consider many different factors including types of credit accounts (mortgage, installment, revolving), outstanding balances and the amount of credit available. These factors are used to predict a consumer's future behavior and how likely a borrower is to make their payments on time.
Credit scoring is industry specific. Student loan models will be different than mortgage models, mortgage scoring models will vary from those used for credit cards. Your score that you get from a free credit score site will vary from the score that I get when I pull a mortgage credit report.
It is possible that you can get different scores within the mortgage industry. Major banks have their own criteria for what makes a more risky borrower. Many lenders and brokers have private companies that they use that have been approved by Fannie Mae, Freddie Mac or FHA. Lenders that use independent credit reporting agencies will usually show similar credit scores.
I have had clients call and say their credit score is "x", so then they are confused when I pull my credit report and the score is lower than they expected. Mortgage models are definitely different than other credit scoring models, so don't be surprised if your lender comes up with a different score than you were expecting. If there is a major difference, then you want to look at your credit report and make sure there aren't errors on it.