How to check a user uses social login

You can add following code in the functions.php file of your active theme to show a new field Social Login User at the user-profile page that shows Yes if that user used social login.

You can check the checkbox Send post-registration email to user to set account password in the Advanced Configuration section at the Social Login configuration page to send an email to the new user to set a password to login via login form at your website. If they use this link to set password, they will be able to login via login form and it won’t affect social login. They can use both the ways to login.

Here is the code.

Thanks, had to change to
<td><?php echo get_user_meta( isset( $_GET['user_id'] ) ? intval( $_GET['user_id'] ) : $user_ID, 'thechamp_social_id', true ) ? __( 'Yes', 'thechamp-social-login' ) : __( 'No', 'thechamp-social-login' ); ?></td>

With setting the checkbox as described above: is this the only possibility a user can have social login and password when they set a password when they receive a mail.

Differently asked, can they, without this mail, set a password and get both?

As this is the support forum for Heateor Social Login plugin, I assumed you were using that plugin.
Yes, even if a user sets password manually at your website after using social login, they won’t lose their ability to social login.