Hello Alejandrino,
The sign up link should redirect to the registration page of Joomla (Assuming that you are integrating the login system with Joomla) while the login page should be redirected to the login layout in Joomla.
You need to ensure that the sign up page can be accessible by public users because there are times when you are brought to the correct page but because of the menu permissions, Joomla is redirecting you to login causing you to think that they are brought to the same page