What is the difference between method and model? I know that OLS is an estimation method. I suppose that OLS models are simply a bunch of variables in one group for which an OLS method is used. Is that correct?
Also, is it wrong to say that negative binomial is a method? I guess so, it's a distribution, right? But then what is the estimation method? E.g. what estimation method am I using when I use glm.nb function in r?
 A: A model is a mathematical description of a problem. In statistics this description is made in terms of probability distributions, random variables, and their functions, but there are also mathematical models outside of statistics that aren’t concerned about random variables. For example, in case of linear regression, we describe the relation between dependent and independent variable in terms of a linear function of independent variables. If we use negative binomial distribution as a model, we assume that the observed variable can be approximated using this distribution, so that the properties of the distribution could be used to describe the data.
What you call a method sounds as an algorithm used for estimating the parameters. OLS is an algorithm that uses linear algebra to minimize the squared error to find the linear function used by linear regression. Another example may be using a black-box optimizer to find a maximum of a likelihood function, to fit the negative binomial distribution to the data.
