die Begleitung
companion
One or more people who accompany someone to a place or event.
Der Minister erschien in Begleitung seiner Frau auf dem Empfang.
The minister appeared at the reception in the company of his wife.

companion / accompaniment
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companion
One or more people who accompany someone to a place or event.
Der Minister erschien in Begleitung seiner Frau auf dem Empfang.
The minister appeared at the reception in the company of his wife.

The noun 'die Begleitung' (companion / accompaniment) is derived directly from the verb 'begleiten' (to accompany). The ending '-ung' turns the verb into a feminine noun that describes the action or its result.
Die Begleitung durch die Polizei sorgte für Sicherheit.
The accompaniment by the police provided security.
When a person is accompanied by another person, you use the fixed expression 'in Begleitung von' (in the company of), followed by a person in the dative.
Die Kanzlerin traf in Begleitung von mehreren Ministern ein.
The chancellor arrived in the company of several ministers.
The context makes clear which meaning is intended. If it is about people, it refers to the accompanying person. Words like 'Klavier' (piano) or 'Gesang' (singing) point to the musical meaning. If it is about a service, it refers to the act of accompanying.
Ihre Begleitung für den Abend war ein alter Schulfreund.
Her companion for the evening was an old school friend.
society / company
'Gesellschaft' and 'Begleitung' can both mean that you are not alone. 'Gesellschaft' emphasizes being together with other people, and often also pleasant social company. 'Begleitung' emphasizes more that someone goes along with you or is present, for example for an appointment, on a trip, or at an event. They can be confused because in both cases other people are there. As a simple guide: you enjoy Gesellschaft, but you take Begleitung with you or need Begleitung.

Heute brauche ich eine Begleitung zum Arzt, weil ich noch unsicher bin.
Today I need someone to accompany me to the doctor because I still feel unsure.
Nach dem Umzug fehlte ihr die Gesellschaft von Freunden und Nachbarn.
After the move, she missed the company of friends and neighbors.