Elongation measurement and displacement-controlled loading are both listed applications, alongside tensile strength and breaking force.
On long specimens, elongation is usually taken over a defined free length rather than a short gauge, and the measurement approach has to suit both the specimen and the method.
Which technique fits depends on the standard you work to and on whether the specimen survives the test. For metallic materials the reference is usually ISO 6892-1 or ASTM E8/E8M, which set out how the gauge length is marked and measured.