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.

'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 mean that something is not moving. 'still' generally describes quietness or lack of movement, for example with a person, an animal, or a room. 'stehend' is more appropriate when something stays in one place and does not flow or move along, for example water or air. Learners may confuse the words because both have to do with 'not moving'. A practical tip: 'still' sounds more general and can also mean 'quiet', while 'stehend' more often describes a fixed state in one place.

In dem alten Eimer war stehendes Wasser.
There was stagnant water in the old bucket.
Das Kind blieb ganz still, als der Hund an ihm vorbeilief.
The child stayed completely still as the dog walked past him.