die Zählung
count
The act of counting in order to determine the exact number of people or objects; a survey or census.
Die Zählung der abgegebenen Stimmen dauerte die ganze Nacht.
The count of the votes cast lasted all night.

count
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count
The act of counting in order to determine the exact number of people or objects; a survey or census.
Die Zählung der abgegebenen Stimmen dauerte die ganze Nacht.
The count of the votes cast lasted all night.

'Die Zählung' (the count) is the nominalization of the verb 'zählen' (to count). It describes the action or process of counting.
Bitte zählen Sie die Gäste, damit wir die genaue Anzahl wissen.
Please count the guests so that we know the exact number.
'Zählung' (count) is often used with a genitive that indicates what is being counted. Typical examples are 'Zählung der Stimmen' (counting of the votes), 'Zählung der Bevölkerung' (census of the population), or 'Zählung der Tiere' (counting of the animals).
Die jährliche Zählung der Vögel im Park hilft den Forschern.
The annual count of the birds in the park helps the researchers.
The meaning in a sports context is easy to recognize from words like 'Boxer' (boxer), 'Ringrichter' (referee), 'Kampf' (fight), or 'am Boden' (on the ground). Outside of boxing, this meaning is not used.
Der Ringrichter begann die Zählung, als der Kämpfer zu Boden ging.
The referee began the count when the fighter went down.
survey / elevation
'die Erhebung' and 'die Zählung' can both have to do with collecting information. 'Erhebung' is broader: many kinds of data can be collected, for example opinions, income, or living conditions. 'Zählung' is narrower and mainly means determining the exact number of people or things. The words can be confused because a count can often be part of a survey. If it is only about the number, 'Zählung' is more precise. If different kinds of data are being collected, 'Erhebung' fits better.

Im Museum beginnt am Abend die Zählung aller Besucher des Tages.
At the museum, the count of all the day's visitors begins in the evening.
Die Stadt startet eine Erhebung, um mehr über die Nutzung der Busse zu erfahren.
The city is starting a survey to learn more about how the buses are used.