How do Umbrellas attach

I was looking and I cant tell.
Do they connect to the light or do they connect onto the stand.
Do all lights have an umbrella hole for them if they connect to the light.

Most studio monolights have a way to attach an umbrella to the monolight's housing. The monolights normally connect to a 5/8" diameter stud on the top of the light stand.

For other types of lighting, you may need to obtain one of several types of mounting adapters to attach equipment to a light stand.

thanks