begrüßen
to greet
To welcome someone during an encounter with a greeting or a gesture.
Der Portier begrüßte jeden Gast mit einem freundlichen Lächeln.
The porter greeted every guest with a friendly smile.

to greet / welcome
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to greet
To welcome someone during an encounter with a greeting or a gesture.
Der Portier begrüßte jeden Gast mit einem freundlichen Lächeln.
The porter greeted every guest with a friendly smile.

'Begrüßen' (to greet / welcome) is an inseparable verb. The prefix 'be-' remains firmly attached to the verb in all tenses and sentence positions.
Er begrüßte seine Kollegen am Morgen.
He greeted his colleagues in the morning.
The verb 'begrüßen' (to greet / welcome) is derived from 'der Gruß' (the greeting). The prefix 'be-' makes the verb transitive, which means it always needs an accusative object to whom the greeting is directed.
Der Redner begrüßte das Publikum.
The speaker greeted the audience.
You can recognize the meaning from the object: if the object is a person, it means 'willkommen heißen' (to welcome). If the object is a thing or a subordinate clause (e.g. a decision, a measure), it means 'gutheißen' (to approve of).
Die Kanzlerin begrüßte den Präsidenten am Flughafen.
The chancellor greeted the president at the airport.
To express that you approve of an action or event, the structure 'es begrüßen, dass ...' (to welcome the fact that ...) is often used. Here, 'es' is a placeholder for the following subordinate clause.
Wir begrüßen es, dass die Stadt mehr in den öffentlichen Nahverkehr investiert.
We welcome the fact that the city is investing more in public transport.
to be called / to mean
'jemanden willkommen heißen' (to welcome someone) and 'begrüßen' both have to do with a friendly reaction to a person who arrives or whom you meet. 'begrüßen' is the normal word for a greeting, for example with 'Hallo', with your hand, or with a smile. 'jemanden willkommen heißen' sounds stronger and often somewhat more official or warmer. You use it when you want to show that a person is truly welcome, for example with guests, new employees, or visitors. In everyday life, people usually say 'begrüßen'; for a special arrival, 'willkommen heißen' fits better.

Meine Mutter begrüßt meinen Freund immer mit einem freundlichen Lächeln.
My mother always greets my friend with a friendly smile.
Der Direktor hieß die neuen Schüler am ersten Schultag willkommen.
The principal welcomed the new students on the first day of school.