What is the difference between module_init and init_module in a Linux kernel module?

If you look at the definition of the new functions:

/* Each module must use one module_init(). */
#define module_init(initfn)                 \
static inline initcall_t __inittest(void)       \
{ return initfn; }                  \
int init_module(void) __attribute__((alias(#initfn)));

/* This is only required if you want to be unloadable. */
#define module_exit(exitfn)                 \
static inline exitcall_t __exittest(void)       \
{ return exitfn; }                  \
void cleanup_module(void) __attribute__((alias(#exitfn)));

You'll see it ensures that the right boilerplate is included so these special functions can be correctly treated by the compiler. It's what the internal API of Linux does, it evolves if there are better ways of solving the problem.

What is the advantage of [module_init] in Kernel 2.6

module_init also exited in 2.4, mind you.

It adds the necessary boilerplate to initialize the module and run the entry function when the module file is compiled into the kernel rather than as a module.