When I convert some data for a model (e.g., wealth, pollution) into per capita figures (e.g., wealth per inhabitant, tons of pollution per inhabitant) is this a transformation or re-expression of the data? Or is the term transformation or re-expression reserved for logarithmic or exponential transformations (including roots and inverses)?
I would say that what you've described is neither transformations nor re-expressions. The wealth of a nation and wealth / inhabitant of a nation (or pollution, etc.) are just different things. They're both about wealth and pollution but they have very different meanings.