Penumbra and umbra are two terms used to describe certain regions of shadow or eclipse. Penumbra refers to a partially shaded area that is formed around the edges of an eclipse or a shadow. When the eclipse is formed, the region with partial illumination is known as the penumbra.
On the other hand, umbra refers to the fully shaded inner part of a shadow. When an eclipse is formed, the region on the earth or moon fully shaded is known as the umbra. In other words, the umbra is known as the central region of a sunspot.
Another difference can be noticed when you consider their sizes with respect to their distance from the sun. Penumbra tends to become bigger when it is far away from the sun. In contrast, the umbra gets smaller with respect to its distance away from the sun. During a solar eclipse, the umbra is usually the dark region, while the other region that is partially shaded is the penumbra.