What is the difference between length measurement and strain measurement?

In principle, one can calculate the strain from a length measurement and, conversely, a length change can be calculated from a strain measurement.

The strain measurement is mainly characterized in that an enlargement or reduction of the strain gauge has no direct influence on the sensitivity of the measurement:

The strain gauge always measures the average (average) strain below its surface.
A smaller strain gauge is particularly suited to refine the local resolution (e.g., near notches), while a large strain gauge primarily provides a mean value over locally varying strain (e.g., fiber composites).

"More measurement signal" due to longer measuring grids, there is no case!