setuid trouble understanding

I read about setuid and I did'nt understand the term in 100%.
As I undetstand: setuid allow users to run an executable with the file system permissions of the executable's owner or group respectively and to change behaviour in directories. (from Wikipedia).

But, I can't see a difference between:

-rwsr--r-- ::: you set to owner (rws is the owner) the setuid, so in other words you set to owner the owner permissions.
so there is no effect, right?

-rwxr--r-- ::: is equal to the previous example, beacuse as I said, already talk about the owner so it's does'nt matter to add the owner the owner permissions.

THANKS FOR HELPS!

When you run a executable with setuid bit enabled, it is run with the identity of the owner instead the user that is running the executable. Thus, if you has a executable which the owner is root and the setuid is enabled, the executable will run as root instead the user that is running the executable.

From man:

   setuid() sets the effective user ID of the calling process.  If
   the calling process is privileged (more precisely: if the process
   has the CAP_SETUID capability in its user namespace), the real
   UID and saved set-user-ID are also set.

   Under Linux, setuid() is implemented like the POSIX version with
   the _POSIX_SAVED_IDS feature.  This allows a set-user-ID (other
   than root) program to drop all of its user privileges, do some
   un-privileged work, and then reengage the original effective user
   ID in a secure manner.

   If the user is root or the program is set-user-ID-root, special
   care must be taken: setuid() checks the effective user ID of the
   caller and if it is the superuser, all process-related user ID's
   are set to uid.  After this has occurred, it is impossible for
   the program to regain root privileges.

   Thus, a set-user-ID-root program wishing to temporarily drop root
   privileges, assume the identity of an unprivileged user, and then
   regain root privileges afterward cannot use setuid().  You can
   accomplish this with seteuid(2).

You can verify this with the following code:

#include <stdio.h>
#include <unistd.h>
#include <stdlib.h>

int main(void){

    int val;
    printf("The real user ID is %d\n", getuid());
    printf("The effective user ID is %d\n", geteuid());

    return 0;

}

Compile and setuid:

gcc uid.c -o uid
sudo chown root.root uid
ls -la uid
-rwxr-xr-x 1 root root 16712 Jul 10 11:59 uid
./uid                   
The real user ID is 1000
The effective user ID is 1000
sudo chmod 4755 uid     
ls -la uid         
-rwsr-xr-x 1 root root 16712 Jul 10 11:59 uid
./uid              
The real user ID is 1000
The effective user ID is 0

You already have a very complete answer from sinkmanu. But maybe an example to clarify why we need SetUID:

Check out the passwd command on your system. As a regular user you can change your password with this command. But to actually do this it has to change system files which are only accessible by root. Normally it would run as your user so it won't be able to access /etc/shadow for example, let alone write to it. But thanks to a SetUID bit the command will actually execute as it's owner which is root.

$ ls -l /usr/bin/passwd
-rwsr-xr-x. 1 root root 33K Feb  7  2022 /usr/bin/passwd*

Note: If you have root access you can create your own SetUID programs. But be aware that this potentially poses a security risk. Security scans will often also scan a system for unknown programs with the SetUID turned on and alert the admins.