Answer
The fundamental difference lies in the arrangement of the waves. In a Crest-to-Crest spring, the waves are in 'series', meaning the total deflection is the sum of the deflections of each turn. The rate is $k_{series} = \frac{k_{single}}{Z}$. In a Nested spring, the turns are in 'parallel', meaning each turn experiences the same deflection and the total force is the sum of the forces. The rate is $k_{parallel} = n \cdot k_{single}$. This means that for the same space envelope, a Nested spring will be many times stiffer than a Crest-to-Crest spring. Specifically, if a spring has 3 turns, the Nested version is 9 times stiffer than the Crest-to-Crest version ($3$ in parallel vs $1/3$ in series). This makes Nested springs suitable for extremely high loads with small deflections, while Crest-to-Crest is for large deflections with lower loads.
