So does Google and Facebook. It’s called Single Sign On (SSO) and none of your account details end up on the 3rd party sites. The way it works is that 3rd party developers first have to register with CCP before they can use SSO. The 3rd party site directs the player to CCP’s login site with a id identifying the 3rd party. CCP then takes your account and password, which only CCP knows, and redirects back to the 3rd party. The 3rd party never gets to see your account name or password. All they get is a security token to a strictly controlled set of data. With the new ESI is this even less information than it used to be. One can now no longer tell who is the alt of whom for example.
You want to go to 3rd Party Developers when you want to know the full details of it.