I've seen some "rivers" that were tiny little things that you could nearly wade across at parts - but they're called rivers. Is it gallons/liters per minute that flow? Some other criteria? ~ FF

I’ve always assumed that the continuous flow of water from source to sea (OK, it could be a lake or another river) would be named as, say, River Idunnowot, even though it became narrower as you moved upstream. But probably this only happened if the mouth was found and named first and exploration moved upstream from there. In many cases rivers were discovered and named in sections or by local communities, and the connection between the sections was only discovered later. In that case the same river would have a number of names along its length. Lesser flows that join it are tributaries but may themselves be rivers if they warrant being called a river at their downstream end. There seems to be no particular standard by which you could say what is a river and what is a stream. It has been a subjective decision and, for example, some UK rivers might never have achieved that status in other, larger countries.

A creek, by the way, holds a different meaning in the UK from that used in the US. This from MW:

Main Entry: creek
Pronunciation: 'krEk, 'krik
Function: noun
Etymology: Middle English crike, creke, from Old Norse -kriki bend
Date: 13th century
1 chiefly British : a small inlet or bay narrower and extending farther inland than a cove
2 : a natural stream of water normally smaller than and often tributary to a river
3 archaic : a narrow or winding passage
- up the creek : in a difficult or perplexing situation

In looking for some distinction between rivers and streams I found a passage with two words new to me:

“Slow-moving lotic ecosystems are very similar to those of lentic environments in terms of aquatic plant and animal life.”

For what it's worth, here is MW again:

Main Entry: lo·tic
Pronunciation: 'lO-tik
Function: adjective
Etymology: Latin lotus, past participle of lavere
Date: 1916
: of, relating to, or living in actively moving water <a lotic habitat>

Main Entry: len·tic
Pronunciation: 'len-tik
Function: adjective
Etymology: Latin lentus sluggish
Date: circa 1938
: of, relating to, or living in still waters (as lakes, ponds, or swamps)