how would you define the extension of a spring?

Answer 1

Assuming I understand your question, you would define "extension of a spring" by exactly the distance it is extended/compressed.

(((((((((((((((() normal (spring is "relaxed")
(((((((() <-- compressed
.........<-----> "compression distance" or "extension"

Answer 2

OK!

By extension, I understand you to be referring to the lengthening of a spring by force according to Hooke's Law. That is simply the displacement of the end of the spring from its equilibrium point at rest.

http://en.wikipedia.org/wiki/Hooke's_law