Execute a function when admin changes the user role

You can use the set_user_role hook, that will only fire when the user role changes:

add_action( 'set_user_role', function( $user_id, $role, $old_roles ) 
{
    // Your code ...

}, 10, 3 );

If you want to restrict this to a profile update, you can use:

add_action( 'set_user_role', function( $user_id ) 
{
    add_action( 'profile_update', function( $user_id )
    {
        // Your code here ...            
    } );

} );