(Note: this answer is somewhat of a guess)
Consider how Prolog determines whether f(a,c) is true or not. It checks the first rule, f(a,b), and doesn’t find a match, but the second rule, f(a,c) matches. Therefore, f(a,c) is true. Furthermore, since there are no more rules for f, there is no point in allowing a backtrack to occur — there are no other possible solutions.
Now consider f(a,b). Prolog will check the first rule, and find a match. Therefore, f(a,b) is true. However, not all rules have been exhausted. Therefore, Prolog will allow the search to continue (if you hit ;). When you do continue the search and backtrack, it will discover that the remaining rules, specifically f(a,c), do not match f(a,b). Therefore, the result is false.