Nailed down is the old fashion way of fastening true, real hardwood to a subflooring. It takes a special nailer that actually attaches a finish nail into the groove area and you have it.
Glued, might not be advisable in the kitchen area with all the chemical spills and stuff. The glue might, MIGHT release when compromised.
Floating is not glued or nailed. There is a membrane that goes between the sub floor and under the hardwood flooring. It does muffle the sound and is not quite as echoing as the others. You can demo the stuff in any wood flooring store.
Just remember, a kitchen is the worst place to have hardwood flooring. it takes an unusual hard punishing and has to be maintained. Do think this over.