registriert
registered
Officially recorded and noted in a list, directory, or system.
Jeder Teilnehmer muss namentlich registriert werden.
Every participant must be registered by name.

registered / noticed
Loading your saved state.
registered
Officially recorded and noted in a list, directory, or system.
Jeder Teilnehmer muss namentlich registriert werden.
Every participant must be registered by name.

'Registriert' (registered) is the past participle of the verb 'registrieren' (to register). It is often used like an adjective, either before a noun or together with the verb 'sein' (to be).
Nur registrierte Benutzer haben Zugriff auf die Daten.
Only registered users have access to the data.
The meaning depends on the context. If it is about official lists, data, or systems, the meaning is 'erfasst' (recorded). If it is about the personal perception of people, it means 'bemerkt' (noticed).
Jedes importierte Produkt muss offiziell registriert werden.
Every imported product must be officially registered.
In an official context, 'registriert' (registered) is often combined with adverbs like 'amtlich' (officially), 'offiziell' (officially), or 'namentlich' (by name). The construction 'als etwas registriert sein' (to be registered as something) is also common.
Der Verein ist jetzt offiziell als gemeinnützig registriert.
The association is now officially registered as a nonprofit.
In the meaning 'wahrnehmen' (to perceive), 'registrieren' (to register/notice) is often combined with things that one takes in through the senses or the mind. Typical nouns are 'Blick' (look), 'Veränderung' (change), or 'Tonfall' (tone of voice).
Ich habe den skeptischen Tonfall in ihrer Stimme sofort registriert.
I immediately noticed the skeptical tone in her voice.
admitted / approved
'registriert' and 'zugelassen' both sound official and often have to do with rules or systems. 'registriert' means that someone or something is recorded in a list or system. 'zugelassen' means that someone or something has official permission, for example for an exam, a degree program, a vehicle, or a product. The words can be confused because people often have to register first in order to be admitted later. But registration alone is not permission. 'registriert' says: you are in the system. 'zugelassen' says: you are allowed to participate, drive, be sold, or be used.

Nach der Anmeldung ist sie im System als Teilnehmerin registriert.
After signing up, she is registered in the system as a participant.
Für die Prüfung bin ich zugelassen, weil alle Unterlagen vollständig sind.
I am admitted to the exam because all the documents are complete.