But what about starters? Lets say that I freeze this 2nd generation yeast, then at a later time, make a 2 stage starter from it and then pitch it. Now, am I pitching a 4th generation yeast (because of the 2 starter stages) or am I pitching a 2nd generation yeast?
There would be no logic in calling a starter step a generation in the sense brewers think of their yeast as a 'generation'.
When we put viable cells into a volume of wort(lets call it a starter) they will bud and create other cells which will likewise bud into more cells and so on. How many times they bud and hence multiply within a single step starter depends on the amount of fermentable sugar in the wort vs the number of cells pitched.
If the yeast pitching rate is high(large number viable cells/ml wort) then there will be likely only one or less new generation created. If the yeast pitching rate is very low then there could be more than one generation of budding.
My view is that if optimum handling practices are maintained with all aspects of the starters (sanitation, yeast health, temperatures, storage methods, etc) there should be minimal stress on the yeast. I would therefore not consider a starter step a generation.
However if care is not taken the yeast can be stressed even in a starter and that will effect their health moving forward. It may not kill them but they might end up as poor specimens to form a base for your future brews.
We often talk of yeast viabilty (are they alive or dead) and calculators estimate this based on age.
One thing that calculators do not estimate and that is the vitality of the living yeast and that depends not only on age but the stress they suffered.