::Yes, ISBN-10 and ISBN-13 do have different check digit calculations; in particular, ISBN-10 was devised in pre-barcode days, and uses a calculation involving modulo 11, so when this yields the final value 10, this is shown as "X". ISBN-13 on the other hand was devised to be compatible with the EAN-13 barcode (which recognises ten unique symbols, with no provision for the letter X), and consequently uses the same check digit calculation as is used to produce the barcode on your cornflakes box. In my experience, whenever I've come across a book with both ISBN-10 and ISBN-13, the check digits rarely match (sometimes they do: ISBN 0-319-22897-5 and ISBN 978-0-319-22897-5). 
 ::To convert an ISBN-10 to ISBN-13: take the first 9 digits of the ISBN-10, prepend them with "978", and then apply the formula here. Doing this for 1-85414-316-6 gives me ISBN 978-1-85414-316-7, so it certainly seems like you took the ISBN-13, including its check digit, but omitted the "978" part.