
der Gruß
greeting
A gesture, words, or a message with which you greet someone, say goodbye, or convey good wishes.
Bitte richte deiner Mutter einen schönen Gruß von mir aus.
Please give your mother my warm regards.
greeting
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greeting
A gesture, words, or a message with which you greet someone, say goodbye, or convey good wishes.
Bitte richte deiner Mutter einen schönen Gruß von mir aus.
Please give your mother my warm regards.

sign-off / closing
A formal or informal closing phrase at the end of a letter or email.
Er beendete die E-Mail mit dem Gruß „Herzliche Grüße“.
He ended the email with the sign-off 'Herzliche Grüße' (Warm regards).
'Der Gruß' (greeting) is the noun for the verb 'grüßen' (to greet). A greeting is the result of the act of greeting someone.
Er bat mich, dich von ihm zu grüßen.
He asked me to give you his regards.
Common verbs used with 'Gruß' (greeting/regards) are 'einen Gruß ausrichten' (to pass on someone's regards) or 'einen Gruß schicken' (to send a greeting/regards).
Kannst du ihm bitte einen lieben Gruß von mir ausrichten?
Can you please give him my warm regards?
As a closing phrase in letters or emails, the word almost always appears in the plural and is combined with an adjective. Typical examples are 'Mit freundlichen Grüßen' (formal: Sincerely/Kind regards) or 'Viele Grüße' and 'Liebe Grüße' (informal: Best regards/Love).
Vergiss nicht, die E-Mail mit „Mit freundlichen Grüßen“ zu beenden.
Don't forget to end the email with 'Mit freundlichen Grüßen' (Sincerely/Kind regards).
greeting
Gruß refers to a specific gesture, utterance, or message used to greet someone. Begrüssung refers more to the overall act or the words used to welcome someone. With spoken words, the meanings can overlap; Begrüssung focuses more strongly on the process.

Der Chef hob die Hand zu einem kurzen Gruß, als die neue Kollegin eintrat.
The boss raised his hand in a brief greeting when the new colleague came in.
Die Begrüssung der neuen Kollegin durch den Chef dauerte nur wenige Sekunden.
The boss’s welcome for the new colleague lasted only a few seconds.