das Register
register
An official directory, list, or book in which specific data is systematically recorded.
Jeder Verein muss in das Vereinsregister eingetragen werden.
Every association must be entered in the register of associations.

register
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register
An official directory, list, or book in which specific data is systematically recorded.
Jeder Verein muss in das Vereinsregister eingetragen werden.
Every association must be entered in the register of associations.

'Register' (register) is closely related to the verb 'registrieren' (to register, to record) and the noun 'die Registrierung' (registration). The basic idea of systematic recording and organizing appears in many of its meanings.
Haben Sie sich schon für den Newsletter registriert?
Have you already registered for the newsletter?
Since 'Register' (register) has many meanings, context is crucial. Is it about offices and lists, music and voice, language, or computer technology? The accompanying words reveal the meaning.
Der Techniker prüfte die Werte in den Registern des Prozessors.
The technician checked the values in the processor's registers.
The idiom 'alle Register ziehen' (to pull out all the stops) means to use all available means and abilities to achieve a goal. It originally comes from organ playing, where pulling out all the stops produces the fullest sound.
Im Wahlkampf hat die Partei noch einmal alle Register gezogen.
In the election campaign, the party pulled out all the stops one more time.
In the meaning 'official directory', 'Register' (register) is often used with verbs like 'führen' (to keep/maintain), 'eintragen' (to enter/register), or 'einsehen' (to inspect/view). Common compounds are 'Handelsregister' (commercial register), 'Vereinsregister' (register of associations), or 'Strafregister' (criminal record).
Jede Geburt wird im Geburtenregister vermerkt.
Every birth is recorded in the birth register.
In a musical context, 'Register' (register) can refer to the range of a voice, e.g. head voice or chest voice, or to the timbres of an organ. Words like 'Stimme' (voice), 'singen' (to sing), 'hoch' (high), 'tief' (low), or 'Orgel' (organ) point to this.
Die Sängerin wechselte mühelos zwischen den Registern ihrer Stimme.
The singer switched effortlessly between the registers of her voice.
When it comes to language, 'Register' (register) refers to the style level that fits a particular situation. Typical verbs in this context are 'wählen' (to choose), 'verwenden' (to use), or 'wechseln' (to switch).
In einem Gespräch mit Freunden verwendet man ein informelles Register.
In a conversation with friends, you use an informal register.
The meaning of 'Register' (register) as part of a computer processor is purely technical language from computer science. Without this technical context, this meaning is very unlikely.
Der Prozessor führt arithmetische Operationen direkt in seinen Registern aus.
The processor performs arithmetic operations directly in its registers.
list
'die Liste' and 'das Register' can both refer to an organized collection of data or names. 'Liste' is neutral and very general. You can quickly write a list, for example with names or tasks. 'Register' is more appropriate when data is recorded systematically and often officially, for example at a government office. It sounds more formal than 'Liste'. The words can be confusing because a register is also a kind of list. In everyday language, however, people usually say 'Liste'; for official or carefully maintained data, 'Register' is more natural.

Die Geburt des Kindes wurde im amtlichen Register eingetragen.
The child's birth was entered in the official register.
Herr Schneider prüft die Liste der Patienten für den Nachmittag.
Mr. Schneider checks the list of patients for the afternoon.