der Herr
Mr.
A formal form of address for a man, often used together with the last name.
Guten Tag, Herr Müller, wie kann ich Ihnen helfen?
Good afternoon, Mr. Müller, how can I help you?

gentleman / Mr.
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Mr.
A formal form of address for a man, often used together with the last name.
Guten Tag, Herr Müller, wie kann ich Ihnen helfen?
Good afternoon, Mr. Müller, how can I help you?

'Herr' belongs to the N-declension. This means it takes the ending '-n' or '-en' in all cases except the nominative singular. A common mistake is forgetting this ending.
Ich spreche mit dem Herrn dort drüben.
I am speaking with the gentleman over there.
The word 'Herr' (gentleman / master / lord) is the root of other words related to power or control. These include the verb 'herrschen' (to rule) and the noun 'der Herrscher' (the ruler).
Der König herrschte über ein großes Reich.
The king ruled over a large empire.
When 'Herr' (Mr.) is used as a direct form of address with a last name, it appears without an article. In letters and emails, the formal salutation 'Sehr geehrter Herr...' (Dear Mr...) is common.
Sehr geehrter Herr Schmidt, anbei sende ich Ihnen die Dokumente.
Dear Mr. Schmidt, I am sending you the documents attached.
In the meaning of 'Gebieter' (ruler) or 'Meister' (master), 'Herr' appears in fixed expressions. Examples are 'sein eigener Herr sein' (to be one's own master) or 'Herr der Lage sein' (to be in control of the situation).
Nach dem Umzug in die eigene Wohnung war er endlich sein eigener Herr.
After moving into his own apartment, he was finally his own master.
You can recognize the religious meaning by the fact that 'Herr' (Lord) is often used with the definite article 'der' and without a name. In this context, the word is often capitalized even when it is not at the beginning of a sentence.
Sie vertrauen auf die Hilfe des Herrn.
They trust in the help of the Lord.
man
'der Mann' and 'der Herr' can both mean an adult male person. 'Mann' is neutral and common in everyday language. 'Herr' sounds more polite or formal, especially with a last name, for example 'Herr Schneider'. Without a name, 'der Herr' can also sound somewhat formal or old-fashioned. Learners may confuse the words because both refer to male adults. In everyday life, people usually say 'Mann'; in forms of address, letters, or polite situations, 'Herr' is more common.

Heute ruft Herr Kaya wegen des Vertrags noch einmal an.
Mr. Kaya is calling again today about the contract.
Der Mann neben mir im Zug las die ganze Fahrt ein Buch.
The man next to me on the train read a book the whole trip.