Hi @chuwen!
Both forms are custom forms, which are probably made by your theme, and we do not have integration for them. By default, the Free version of the plugin only displays the buttons in the WordPress default login and register forms, so by default the buttons should not appear in any of the forms.
Our button only appears in the register form because that form probably uses one of the actions used by the WordPress default login or register form, but it seems that the login form does not.
If you want to show the button in your login form as well then you have 2 options:
A.) If you are able to edit the contents of the form, you could try using our shortcode: https://nextendweb.com/nextend-social-login-docs/usage/
B.) Check the source code of the form if it has a login form specific action. If that’s the case, then you could hook a function there where you render the buttons with PHP code: https://nextendweb.com/nextend-social-login-docs/usage/#php-example
