Think just shadows.......the penumbra is not the specular light, if you will....
Umbra is a shadow that virtually has NO LIGHT
Penumbra is the shadow part that actually would have detail or receive some light.
In a ring light shadow, clearly examined, you would find this.
In my image notice the light on Kelly's cheek gradually fade into a penumbra shadow into an umbra ...... Look at the chair, look at her arms, look at her legs, look everywhere that you see a light fall off that creates the penumbra into the umbra. So in conclusion the penumbra would always surround the umbra if a penumbra existed....in more directional light souces such as parabolox flash reflector heads, umbrellas, grids, etc, you would have more definition of an umbra or sharper edge umbra and less of a penumbra shadow.
Now here is where it gets confusing...The farther your light source is away, you would have sharper more defined umbras.