der Gurt
seat belt
A safety belt in a vehicle such as a car or airplane, intended to protect occupants in an accident.
Bitte legen Sie den Gurt an, bevor wir losfahren.
Please fasten your seat belt before we set off.

belt / strap
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seat belt
A safety belt in a vehicle such as a car or airplane, intended to protect occupants in an accident.
Bitte legen Sie den Gurt an, bevor wir losfahren.
Please fasten your seat belt before we set off.

In a car or airplane, the verbs 'den Gurt anlegen' (to fasten one's seat belt) or 'sich anschnallen' (to buckle up) are used for a seat belt. The state is described with 'angeschnallt sein' (to be buckled up).
Der Flugbegleiter bat alle Passagiere, den Gurt anzulegen.
The flight attendant asked all passengers to fasten their seat belts.
'Gurt' (belt/strap) is the basic word for many specific straps or belts. Depending on the context, it is often combined into a more precise word, e.g. 'der Sicherheitsgurt' (seat belt, in a car), 'der Spanngurt' (tie-down strap, for cargo), or 'der Klettergurt' (climbing harness, in sports).
Für den Umzug brauchen wir stabile Spanngurte, um die Möbel zu sichern.
For the move, we need sturdy tie-down straps to secure the furniture.
When a strap is used to fasten objects, typical verbs are 'festziehen' (to tighten), 'lockern' (to loosen), or 'umlegen' (to put around).
Kannst du den Gurt um den Schlafsack noch etwas fester ziehen?
Can you tighten the strap around the sleeping bag a bit more?
ribbon / band
'das Band' and 'der Gurt' can both be a long strip of material. The difference is mainly in function and strength. A 'Band' is often narrower or lighter and is used for tying, decorating, or simple technical purposes. A 'Gurt' is usually stronger and is meant to secure, hold, or carry something. That is why in a car or airplane you say 'Gurt', not 'Band'. Learners may confuse the words because both can look similar, but 'Gurt' clearly suggests safety and load-bearing.

Im Auto lege ich immer den Gurt an, bevor wir losfahren.
In the car, I always fasten my seat belt before we set off.
Der Lehrer hat ein rotes Band um das Geschenk gebunden.
The teacher tied a red ribbon around the gift.