gleichbedeutend mit
synonymous with
Having exactly the same meaning; to be synonymous.
Das Wort 'Auto' ist in vielen Kontexten gleichbedeutend mit 'Wagen'.
In many contexts, the word 'Auto' (car) is synonymous with 'Wagen' (car/vehicle).

synonymous / equivalent
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synonymous with
Having exactly the same meaning; to be synonymous.
Das Wort 'Auto' ist in vielen Kontexten gleichbedeutend mit 'Wagen'.
In many contexts, the word 'Auto' (car) is synonymous with 'Wagen' (car/vehicle).

The word is made up of 'gleich' (same/equal) and 'bedeutend' (meaning/significant, from 'bedeuten' (to mean)). It therefore describes that two things have the same meaning.
In diesem Zusammenhang sind die beiden Begriffe fast gleichbedeutend.
In this context, the two terms are almost synonymous.
This adjective is almost always used with the preposition 'mit' and the dative. The structure is: 'Etwas ist gleichbedeutend mit etwas anderem.' (Something is synonymous/equivalent with something else.)
Ein Lächeln ist nicht immer gleichbedeutend mit Freude.
A smile is not always equivalent to joy.
When it is about words or symbols, the literal meaning (m01) is meant. When it is about actions or events, the consequences or effect (m02) are meant.
Das Wort „schnell“ ist gleichbedeutend mit „rasch“.
The word 'schnell' (fast) is synonymous with 'rasch' (quickly).
In this meaning, a negative or drastic consequence is often emphasized. It describes that an action has the same result as another, often worse event.
Den Vertrag nicht zu unterschreiben, ist gleichbedeutend mit einer Kriegserklärung.
Not signing the contract is equivalent to a declaration of war.
immediate / same
'gleich' and 'gleichbedeutend' both have to do with agreement or equivalence. 'gleich' is broader: two things can look the same, be the same size, or have the same value. 'gleichbedeutend' is used when two words have the same meaning or when one thing has practically the same effect as another. Learners may confuse the words because both express 'not different'. But 'gleichbedeutend' is especially suitable for meaning or consequence and is often used with 'mit'.

Für meinen Kollegen ist eine Absage gleichbedeutend mit einem neuen Plan.
For my colleague, a rejection is equivalent to a new plan.
Die beiden Schlüssel sehen gleich aus, aber nur einer passt zur Tür.
The two keys look the same, but only one fits the door.