What is the difference between fixed-rate mortgages and subprime loans ?
There doesn't technically have to be a difference. They refer to two separate things. Whether or not a rate is fixed has to do with the TERMS of the loan.
And Subprime is simply a name given to certain types of loans that are considered to be of a higher credit risk than other loans. The loan tiers that people normally discuss are sub-prime (the worst), Alt-A (the middle), and conforming (the best).
Sub-Prime also refers to the types of loans offered by lenders. It's possible to have a sub-prime lender do a loan for someone with a very high credit score. Sub-prime lenders offer fixed rate mortgages, as do Alt-A, and Conforming lenders.
In sub-prime, you might expect the rate to be higher on a 30 year fixed loan than you would on a conforming loan.
Also keep in mind that "fixed rate" doesn't mean much any more as there are 5 year adjustable loans that have a fixed rate for five years, yet adjust after that. These can be advertised as " five year fixed." Always make sure you know the total length of the loan, and the total length of the fixed period.