A stream runs a little faster,may have little falls and pools.
A brook runs on the flattest ground of all these waterways you mention,it kind of meanders.
A creek is very like a stream but even faster,though less reliable as it can dry up...it's often run-off from the snow.
A river is the culmination of all these waterways...they all eventually flow into the river,which usually flows (slow and/or fast) to a lake,sea,or ocean.