A First Time Buyer mortgage is not magically different from other mortgages- neither is it legally different. It is usually just a better deal than a lender’s other mortgages, because (just like banking) once you’ve signed up, you’re less likely to leave. That makes you, the first time buyer, a great customer for a lender to have on their books.
That said, First Time Buyer mortgages are also usually structured to offer greater benefits in the first few years, where the customer is likely to need money for e.g. furniture, and also likely to be younger and therefore less well off in general. These benefits can include one or more of a lump sum back upon completion, a discounted interest rate (or stepped rate), or indeed a fee-free transaction.
However, don’t feel that as a first time buyer, you’re restricted to a First Time Buyer mortgage- there’s no substitute for checking the best rates, assessing the true cost of a product, and plumping for the one that’s right for you. If you’re buying a house to live in for a couple of years, knowing full well that you’re then going to emigrate to Australia on the profit you make from your house; a five year fixed deal won’t be right for you, whether it’s got “First Time Buyer” stamped on it or not.
Almost all lenders offer some sort of first time buyer mortgage package- so ask around, and extort the best benefits package you can get.