Kaplan-Meier vs Nelson-Aalen


Working on survival analysis on a bunch of cows that suffer from a common form of disease. I'm trying to get into an analysis pattern here... By the way, I'm using STATA.

I'm just refreshing my memory (not the greatest stats person, self taught thus far), K-M and N-A -->

So Kaplan-Meier survival function estimates median survival time of the population. N-A estimates the cumulative hazard function? I don't get it, are they always analyzed, one after the other? Like, when i find out from my dataset, the median survival of my population of cows, I will need to proceeed to find the cumulative hazard function of the population?? How do I define the cumulative hazard - "hazard" as in to contract the disease of interest, or "hazard" as in to be removed from the milking herd??

I read somewhere N-A is for small data set versus K-M is for larger sets. How does one define small versus large?


Input most welcomed