der Kellner
waiter
A male person who serves guests in a restaurant, café, or bar, takes orders, and serves food and drinks.
Der Kellner brachte uns die Speisekarte und empfahl den Wein.
The waiter brought us the menu and recommended the wine.

waiter
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waiter
A male person who serves guests in a restaurant, café, or bar, takes orders, and serves food and drinks.
Der Kellner brachte uns die Speisekarte und empfahl den Wein.
The waiter brought us the menu and recommended the wine.

The word 'Kellner' (waiter) is derived from 'der Keller' (cellar). Historically, the waiter was responsible for the wine and beverage cellar of a house or inn.
Der Kellner empfahl uns einen ausgezeichneten Wein aus dem Keller des Hauses.
The waiter recommended an excellent wine from the house cellar.
When interacting with a waiter, you often use fixed phrases. You 'call' the waiter (accusative), 'ask him about' something (accusative), or 'give him' a tip (dative).
Könnten Sie bitte den Kellner rufen?
Could you please call the waiter?
Especially in Austria, the term 'der Ober' is often used instead of 'Kellner' (waiter). The form of address is then usually 'Herr Ober'.
„Herr Ober, die Rechnung bitte!“, rief der Gast im Wiener Café.
'Waiter, the bill please!' called the guest in the Viennese café.
innkeeper / host
'der Wirt' and 'der Kellner' both belong in the context of a restaurant or pub, but they have different roles. 'der Wirt' owns or runs the establishment. So he is responsible for the business. 'der Kellner' serves the guests, takes orders, and brings food or drinks. The words can be confused because both people work in the same place and deal with guests. In practical terms: the waiter comes to the table; the innkeeper runs the place.

Der Kellner bringt uns die Speisekarte und nimmt später die Bestellung auf.
The waiter brings us the menu and later takes our order.
Der Wirt begrüßt die Stammgäste persönlich an der Tür.
The innkeeper personally greets the regular guests at the door.