@Atefeh after talking with the team who maintains the value_count agg, it seems my initial assumption was wrong, and it should be an exactly count - NOT approximate. It may be that you've found a bug, or that your cluster is having issues.
Can you share some more info?
- what version of Elasticsearch are you using?
- can you reproduce on another index? If so, can you provide the reproduction steps?
- can you share the full output of your responses that differ, and show that there are not any partial shard failures?
- can you check the Elasticsearch logs during the query and share if there are any errors or warnings?