Both use strong light-dark contrast. Chiaroscuro is the general technique; tenebrism is its extreme, where darkness dominates the whole scene and figures seem spotlit out of black.
Side by side
Aspect
Chiaroscuro
Tenebrism
Contrast
Strong
Extreme
Darkness
Present
Dominates
Relationship
The broad technique
A subset of it
Feel
Volume, depth
Drama, menace
What each one means
Chiaroscuro
Chiaroscuro is the dramatic use of strong contrast between light and dark. In art, film, and writing, it's how a single source of light carves shape, tension, and mood out of surrounding shadow. In its narrower art-historical sense it is simply the modelling of three-dimensional form with light and shade — as in a chiaroscuro drawing or woodcut.