Why is it called the score of the log likelihood function? Since the score of the log likelihood function is just the gradient of the log likelihood function, why give it a special name? Why not just call it the gradient?
 A: I've never before heard it called the "score of the log-likelihood function" or the score of anything in particular.  If you call something a gradient you have to (at least tacitly) say that it's the gradient of something.  Calling something the score means it's the gradient of the log-likelihood function.
A: I was wondering the same thing. After a bit more digging, I found an answer on stats.stackexchange.com, so I figured I might as well share here for anyone who finds this question first: https://stats.stackexchange.com/questions/326091/interpretation-of-score. I will quote as a summary:

the term "score" initially arose as a term that Fisher used in a specific application of statistics to a problem involving the genetic properties of children in a family. He estimated a genetic probability by giving each family a "score" based on the number of children in four categories of interest. The term was then deployed more broadly by other authors to refer to what Fisher had called the "ideal score", which was the derivative of the log-likelihood.

