Is "Hush a bye baby" a Nursery Rhyme or lullaby?

The words and origin of the "Hush a bye baby" rhyme are said to have originated from America.
 

It was the practice of some Native Americans to place a baby in the branches of a tree allowing the wind to gently rock the child to sleep "Hush a bye baby on the treetop".
 

The meaning to the words of the song "Hush a bye baby" seem to match this explanation.
 

The words to the "Hush a bye baby" song have the intention of making a child sleep it can therefore be correctly described as both a nursery rhyme and a lullaby!
 

The words to the "Hush a bye baby" song were first published in 1765.