
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.

supple
Feeling soft and smooth, often in reference to skin or leather.
Die Creme macht die Haut wieder geschmeidig.
The cream makes the skin supple again.

chill / smooth
Colloquial for smooth, uncomplicated, or relaxed.
Bleib mal geschmeidig, das kriegen wir schon hin.
Just stay chill; we'll manage it.
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!
smooth / slippery
Glatt describes an even, non-rough surface. When used for skin or leather, geschmeidig additionally means that the material feels soft and supple. A firm surface can therefore be glatt; for soft, flexible leather, geschmeidig is a better fit.

Das Leder der neuen Handschuhe ist weich und geschmeidig.
The leather of the new gloves is soft and supple.
Die Oberfläche des neuen Ledergürtels ist ganz glatt.
The surface of the new leather belt is completely smooth.