What makes a bayou is that it is a distributary, not a tributary. Way upstream all the little creeks feed into rivers and into the Big river, these are tributaries.

Downstream, there is so much water to get to the sea that some of it breaks out into birdsfoot shaped networks of smaller streams called distributaries. These are bayous. Some are big, some smaller.

These things are very gentle in their grade and tend to lay sediment down rather than scour it out. This why our channelling the Mississippi and generally jacking with it is one of the interrelated causes of coastal erosion in Louisiana. There is no longer the volume of sediiment being laid down in the bayous to compensate for coastal and other erosional forces and we get a net loss of land.