Inner work
Inner work means looking at what goes on inside you, so it runs you a little less. Your reactions, your old stories, your habits, the way your body tenses up. It's slow and honest, and you do it on purpose.
For exampleYou snap at your partner over something small. Later, you sit down and ask what actually got touched in you.
Shadow work
The idea of the shadow comes from Carl Jung, the Swiss psychiatrist. He used it for the parts of ourselves we don't see, or have pushed away because they felt unacceptable: anger, need, envy, weakness, desire. The shadow can hold good things too, like strength or confidence you learned to hide. Shadow work is a modern name for turning towards those parts, so they leak out sideways less often.
For exampleA man who brags really gets under your skin. When you look closer, you might find a part of you that wants to be seen and has never let itself ask for it.