
stehend
standing
Being in an upright, vertical position, not sitting or lying down.
Nach dem Konzert gab es stehende Ovationen für die Band.
After the concert, there was a standing ovation for the band.
standing
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standing
Being in an upright, vertical position, not sitting or lying down.
Nach dem Konzert gab es stehende Ovationen für die Band.
After the concert, there was a standing ovation for the band.

stagnant / still
Not moving; stationary. Often used for bodies of water or air.
Stehende Gewässer sind ein idealer Brutplatz für Mücken.
Stagnant bodies of water are an ideal breeding ground for mosquitoes.

fixed / established
In a figurative sense: fixed, established, and generally known.
„Eulen nach Athen tragen“ ist eine stehende Redewendung.
'Eulen nach Athen tragen' (to carry owls to Athens) is a fixed expression.
'Stehend' (standing) is the present participle of the verb 'stehen' (to stand). It functions like an adjective and describes a person or thing that is currently in the state of standing.
Der stehende Zug wartete auf das Signal zur Abfahrt.
The stationary train waited for the signal to depart.
A very fixed and common collocation is 'stehende Ovationen' (standing ovation). This means that the audience stands up to applaud enthusiastically.
Nach dem beeindruckenden Konzert gab es für die Musiker stehende Ovationen.
After the impressive concert, there was a standing ovation for the musicians.
In this meaning, 'stehend' (stagnant/still) is almost always used for things that could normally move but do not. Typical examples are 'stehende Luft' (stagnant air, in a room without ventilation) or 'stehende Gewässer' (stagnant bodies of water, such as a pond or puddle).
Im Sommer kann die stehende Luft in der Stadt sehr unangenehm sein.
In summer, the stagnant air in the city can be very unpleasant.
In the figurative sense, 'stehend' (fixed/established) describes something fixed and unchanging in the linguistic or conceptual sphere. Common combinations are 'eine stehende Redewendung' (a fixed expression) or 'ein stehender Begriff' (an established term).
„Den Nagel auf den Kopf treffen“ ist eine stehende Redewendung im Deutschen.
'Den Nagel auf den Kopf treffen' (to hit the nail on the head) is a fixed expression in German.
quiet / still
Still and stehend can both express a lack of movement in water or air. Still tends to emphasize calmness or the absence of sound, while stehend specifically refers to a lack of flow or exchange. Use stehend when describing water or air as not flowing.

In dem alten Eimer stand das Wasser seit Tagen.
The water had been standing in the old bucket for days.
Am frühen Morgen lag der See ganz still und ruhig vor uns.
Early in the morning, the lake lay perfectly still and calm before us.