The Discord server isn't connected to this forum, or the Planetside website, so it won't ever ask for those logins.
After you sign up and log in to the main Discord app, you can then join individual communities or servers, of which the Terragen Discord is one. The individual servers can have their own user verification process to keep out spammers, and in the case of the Terragen Discord it's cranked up pretty high (as a knee jerk reaction to how much spam this forum used to get). After joining the server, you click the verification button, which takes you to a website to complete a captcha, and then gives you full access to the server. If I remember correctly I think the captcha website asks to connect to Discord during that process as well.
It's kind of a pain the first time, but you should only have to verify once.