module_init macro vs init_module function for built-in kernel modules

I've been trying to do some light kernel development on Android.

I'm a bit confused about how built-in, built using

obj-y += module_name.o

kernel modules use the module_init() macro vs the init_module() function.

I have the two following simple modules, first one:

#include <linux/module.h>
#include <linux/kernel.h>
int init_module(void){
    printk(KERN_ALERT "This is our first program.");
    return 0;
}
void cleanup_module(void){
    printk(KERN_ALERT "End of our first program.");
}

And second one

#include <linux/init.h>
#include <linux/module.h>
#include <linux/printk.h>

static int __init test_module_init(void)
{
    pr_warn("Hello, world\n");

    return 0;
}

module_init(test_module_init);

static void __exit test_module_exit(void)
{
    pr_warn("Goodbye\n");
}

module_exit(test_module_exit);

When I compile the kernel with both modules built-in, the second module is the one that shows a message in dmesg. However, the first module does not.

However, if compile the first module separately and load the *.ko file using insmod ./module_name.ko the first module does print messages to dmesg.

Is this because the module_init() macros are needed to use the load the ELF of the kernel modules during boot time? While the insmod loads the ELF dynamically from within the *.ko file so we don't need to 'register' it using module_init() macro?