What are the major differences between ANSI C and K&R C?

There may be some confusion here about what "K&R C" is. The term refers to the language as documented in the first edition of "The C Programming Language." Roughly speaking: the input language of the Bell Labs C compiler circa 1978.

Kernighan and Ritchie were involved in the ANSI standardization process. The "ANSI C" dialect superceded "K&R C" and subsequent editions of "The C Programming Language" adopt the ANSI conventions. "K&R C" is a "dead language," except to the extent that some compilers still accept legacy code.

Function prototypes were the most obvious change between K&R C and C89, but there were plenty of others. A lot of important work went into standardizing the C library, too. Even though the standard C library was a codification of existing practice, it codified multiple existing practices, which made it more difficult. P.J. Plauger's book, The Standard C Library, is a great reference, and also tells some of the behind-the-scenes details of why the library ended up the way it did.

The ANSI/ISO standard C is very similar to K&R C in most ways. It was intended that most existing C code should build on ANSI compilers without many changes. Crucially, though, in the pre-standard era, the semantics of the language were open to interpretation by each compiler vendor. ANSI C brought in a common description of language semantics which put all the compilers on an equal footing. It's easy to take this for granted now, some 20 years later, but this was a significant achievement.

For the most part, if you don't have a pre-standard C codebase to maintain, you should be glad you don't have to worry about it. If you do--or worse yet, if you're trying to bring an old program up to more modern standards--then you have my sympathies.

There are some minor differences, but I think later editions of K&R are for ANSI C, so there's no real difference anymore.
"C Classic" for lack of a better terms had a slightly different way of defining functions, i.e.

int f( p, q, r )  int p, float q, double r;  {      // Code goes here  }

I believe the other difference was function prototypes. Prototypes didn't have to - in fact they couldn't - take a list of arguments or types. In ANSI C they do.