geschmeidig
supple
Soft, flexible, and elastic in movement or texture. Often describes bodies, materials, or sequences of movement.
Die Katze bewegte sich geschmeidig durch den Garten.
The cat moved supplely through the garden.

supple / smooth
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supple
Soft, flexible, and elastic in movement or texture. Often describes bodies, materials, or sequences of movement.
Die Katze bewegte sich geschmeidig durch den Garten.
The cat moved supplely through the garden.

A very common construction with this adjective is 'jemanden/etwas geschmeidig machen' (to make someone/something supple) or 'halten' (to keep). This describes the process of making something soft and flexible or keeping it in that state.
Regelmäßiges Dehnen hält die Muskeln geschmeidig.
Regular stretching keeps the muscles supple.
In relation to movements, 'geschmeidig' (supple) is often used for animals (especially cats), dancers, or athletes. Typical combinations are 'geschmeidige Bewegungen' (supple movements) or 'ein geschmeidiger Körper' (a supple body).
Der Panther bewegte sich geschmeidig durch den Dschungel.
The panther moved supplely through the jungle.
In the meaning of 'entspannt' (relaxed) or 'reibungslos' (smooth), 'geschmeidig' is purely colloquial. It is used mainly by younger people in informal conversations.
Die ganze Organisation lief total geschmeidig ab.
The whole organization went totally smoothly.
The phrase 'Bleib geschmeidig!' is a fixed colloquial expression. It means something like 'Don't get upset!', 'Stay cool!', or 'Take it easy!'.
Hey, bleib geschmeidig, es ist doch nichts passiert!
Hey, stay chill, nothing happened!
relaxed
'entspannt' and 'geschmeidig' can both express that something is casual and without stress. 'entspannt' is the normal word for this and fits people, situations, and atmosphere well. 'geschmeidig' can also colloquially mean 'smooth' or 'uncomplicated', but it sounds more casual and a bit more figurative. In other meanings, 'geschmeidig' means more like soft, flexible, or smooth, for example with movements or material. Learners may confuse the words when 'geschmeidig' is used in this casual sense. The safer rule is: for calm and low stress, use 'entspannt'; for a process that works smoothly, 'geschmeidig' can fit.

Die Vorbereitung für die Feier lief überraschend geschmeidig.
The preparations for the party went surprisingly smoothly.
Nach dem Spaziergang am Abend war Lisa wieder ganz entspannt.
After the evening walk, Lisa was completely relaxed again.