die Fluglinie
airline
A company that offers commercial flights for passengers or freight; an airline company.
Wir haben bei einer günstigen Fluglinie gebucht, um nach Portugal zu fliegen.
We booked with a budget airline to fly to Portugal.

airline
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airline
A company that offers commercial flights for passengers or freight; an airline company.
Wir haben bei einer günstigen Fluglinie gebucht, um nach Portugal zu fliegen.
We booked with a budget airline to fly to Portugal.

The word is made up of 'Flug' (flight, from fliegen — to fly) and 'Linie' (line). So it figuratively describes a line or route that is flown, and the company that operates it.
Diese Fluglinie bietet Direktflüge nach New York an.
This airline offers direct flights to New York.
Common verbs in connection with 'Fluglinie' (airline) are 'mit einer Fluglinie fliegen' (to fly with an airline) and 'bei einer Fluglinie buchen' (to book with an airline). It is also often described with adjectives such as 'günstig' (cheap / budget), 'bekannt' (well-known), or 'sicher' (safe).
Ich fliege immer mit derselben Fluglinie.
I always fly with the same airline.
Pay attention to the prepositions: You fly 'mit' (with) an airline, but you book a flight 'bei' (with / through) an airline.
Er hat seinen Flug direkt bei der Fluglinie gebucht.
He booked his flight directly with the airline.
airline
'die Airline' and 'die Fluglinie' can both mean a company that offers flights. That is why they are very close in many travel situations. 'Airline' is an international loanword and sounds especially natural in advertising, apps, and travel portals. 'Fluglinie' is a German word and is also used for an airline. Learners can easily confuse the words because both can point to the same company. In normal conversations, 'Airline' is often very common; 'Fluglinie' sounds a bit more German and matter-of-fact.

Im Gespräch empfiehlt der Kollege eine günstige Fluglinie für die Reise.
In the conversation, the colleague recommends a cheap airline for the trip.
In der App sehe ich, welche Airline morgen nach Madrid fliegt.
In the app, I can see which airline is flying to Madrid tomorrow.