The exposure adjustment is a very well defined operation: it consists of multiplying the rgb values by a common factor in the linear camera color space.
On the other hand, I do not think there is a unique definition of brightness. As far as I know, Photoshop (and gimp?) adds a constant value to the rgb values. This is usually applied in the working rgb color space, and the result depends on the gamma encoding that is used. Adding a constant to linear rgb values gives a different result compared to the same constant added to gamma-encoded rgb values.
I think that darktable defines “brightness” as a gamma correction applied to the Lab L channel. As such, it preserves both the black and white points… @houz can probably give a more precise statement.