No, a stream is actually smaller than a river.
brook
The middle part of a river may be called mid-stream, mid-river or mature river.
A large natural stream, which may be a waterway.
It is called a "meander". They are the curved parts in a stream.
Tributary is the answer you are looking for, I believe.
A Tributary
STREAM
A tributary.
The mouth of a river is the outlet.
In the Cayuga (Gayogoho:no') language, the common word for a creek, river or stream is gihęde.
* Brook * Stream * River * Creek
A river mouth is a portion of a stream where it merges with another stream. Note that here the definition of stream is not "a small river", but "any flowing current within well defined banks."