What is the difference between goto and longjmp() and setjmp()?

A goto statement implements a local jump of program execution, and the longjmp() and setjmp() functions implement a nonlocal, or far, jump of program execution. Generally, a jump in execution of any kind should be avoided because it is not considered good programming practice to use such statements as goto and longjmp in your program.

A goto statement simply bypasses code in your program and jumps to a predefined position. To use the goto statement, you give it a labeled position to jump to. This predefined position must be within the same function. You cannot implement gotos between functions.

 When your program calls setjmp(), the current state of your program is saved in a structure of type jmp_buf. Later, your program can call the longjmp() function to restore the program’s state as it was when you called setjmp().Unlike the gotostatement , the longjmp() and setjmp() functions do not need to be implemented in the same function. However, there is a major drawback to using these functions: your program, when restored to its previously saved state, will lose its references to any dynamically allocated memory between the longjmp() and the setjmp(). This means you will waste memory for every malloc() or calloc() you have implemented between your longjmp() and setjmp(), and your program will be horribly inefficient. It is highly recommended that you avoid using functions such as longjmp() and setjmp() because they, like the gotostatement, are quite often an indication of poor programming practice.

How does throwing and catching exceptions differ from using setjmp and longjmp?

The throw operation calls the destructors for automatic objects instantiated since entry to the try block.

Exceptions are in the mainstream of C++ now, so most programmers, if they are familiar with setjmp and longjmp, should know the difference. Both idioms return a program from the nested depths of multiple function calls to a defined position higher in the program. The program stack is "unwound" so that the state of the program with respect to function calls and pushed arguments is restored as if the calls had not been made. C++ exception handling adds to that behavior the orderly calls to the destructors of automatic objects that were instantiated as the program proceeded from within the try block toward where the throw expression is evaluated. 
It's okay to discuss the notational differences between the two idioms. Explain the syntax of try blocks, catch exception handlers, and throw expressions. Then specifically address what happens in a throw that does not happen in a longjmp. Your answer should reflect an understanding of the behavior described in the answer just given.
One valid reason for not knowing about exception handling is that your experience is exclusively with older C++ compilers that do not implement exception handling. I would prefer that you have at least heard of exception handling, though.
It is not unusual for C and C++ programmers to be unfamiliar with setjmp/ longjmp. Those constructs are not particularly intuitive. A C programmer who has written recursive descent parsing algorithms will certainly be familiar with setjmp/ longjmp. Others might not, and that's acceptable. In that case, you won't be able to discuss how setjmp/longjmp differs from C++ exception handling, but let the interview turn into a discussion of C++ exception handling in general. That conversation will reveal to the interviewer a lot about your overall understanding of C++.