Difference between count() and find().count() in MongoDB

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db.collection.count() and cursor.count() are simply wrappers around the count command thus running db.collection.count() and cursor.count() with/without the same will return the same query argument, will return the same result. However the count result can be inaccurate in sharded cluster.

MongoDB drivers compatible with the 4.0 features deprecate their
respective cursor and collection count() APIs in favor of new APIs for
countDocuments() and estimatedDocumentCount(). For the specific API
names for a given driver, see the driver documentation.

The db.collection.countDocuments method internally uses an aggregation query to return the document count while db.collection.estimatedDocumentCount/ returns documents count based on metadata.

It is worth mentioning that the estimatedDocumentCount output can be inaccurate as mentioned in the documentation.

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