Is there any specific difference between a "distribution" and a "family" of distributions? Do we have to say that N(mu,sigma^2) is a family because it's indexed by two parameters? Or can one say that it's a distribution indexed by two params? Wikipedia says things like "gamma distribution is a two-parameter family...", but at the same time "binomial distribution with parameters n and p is the discrete probability distribution..." so it's not very consistent.
Intuitively I would say that if it's is indexed by a finite set of numbers then it's a distribution with parameters, and if it's indexed by infinite-dimensional set of functions (like exponential family) then it's a "family". But that's just what I made up, not something I've ever seen defined.
