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While we don't specify where each query operator can be used, we do specify that:
$match takes a document that specifies the query conditions. The query syntax is identical to the read operation query syntax.
as well as
$match uses standard MongoDB queries.
Whereas for $project, we do specify that with
<field>: <expression>
the expression is linked to aggregation expressions (which lists the accepted aggregation expressions)
http://docs.mongodb.org/manual/meta/aggregation-quick-reference/#aggregation-expressions
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