Those aren’t eID. They are a way to authenticate using CSAM.
There are different weights tied an authentication method, card reader scores highest.
From the top of my head there’s email, sms, totp, card reader, eiDAS and itsme® (which I avoid because it’s proprietary and controlled by a 3rd party).
There’s a list of properties a service can request when accessing data via ACM/IDM, for example your ssn, name, etc.
You can read your eID with local software too, with the aptly named eid viewer. Click on the picture in the overview and drag it into a text editor to see the entire exportable xml.
That’s actually a choice made by the service. The onboarding document has the options listed and they get to choose, which is imho stupid. Just offer all options.
Service A has email enabled, service B doesn’t. Since ACM/IDM is SSO you can first authenticate with service A with your email code and then go to service B already authenticated.