I'm just really confused about the two log in options.
Be careful about connecting up to the wrong platform.
There are two levels of authentication.
Top layer - 1) login to EDSM to retrieve you commander profile - i.e. what EDSM knows about you, which expeditions you attend, what systems you visit
Secondary layer - 2) Elite Dangerous server authentication. - i.e. what the game knows about you. This is platform specific. If you link to the wrong platform, everything will report successfully but you wont get your details to populate the EDSM profile. For PS4, you should be click on playstation logo and using your sony credentials. If you get this wrong, you will be pulling back either Xbox or PC commander details (which will be empty).
I originally signed up from my PS4 account at the start of Distant Worlds II and it was a lot clunkier then. I can't speak for a new user, connecting now but it looks a lot more straight forward. For example - in the early days, you needed to have the console updater active on a second screen (iphone or Ipad) for updates to be imported. At least now, historic information is periodically pulled through.
(You may need to disconnect a previously validated authentication if you have, for instance, connected up to the Frontier servers as a PC commander instead of a PS4 commander.)