I am fuzzy on the distinctions between sampling strata and sampling clusters. Both seem to aim at designs aiming at creating useful estimates of between/within group (strata, cluster) variation, and in particular, seem to be driven by homogeneity due to some shared group definition.
What are the methodological distinctions?
I would find answers to this part of my question most worthwhile if they explicitly address both (i) what stratified sampling and cluster sampling are intended to accomplish, and (ii) their similarities and distinctions.
What are the conceptual distinctions?
As I am an epidemiologist, I would find answers to this part of my question most worthwhile if couched in substantive theories of the concept of a population as a group of individuals sharing multiple overlapping contexts, with overlapping histories of those contexts. For example, with respect to both cluster sampling, and stratification imply for
- Representation in the variables categories? (I.e. valid and reliable estimates.)
- Characterization of inequities between variable categories.
- Are the variable categories the targets of inference?
- Questions of heterogeneity or homogeneity aside, would would preclude a categorical variable from being used?
- What circumstances would lead a study designer to say "You know what? We need an additional variable to cluster sample/stratify on.
EDIT 7-20-2020: I feel all four answers to date address methodological concerns, and only one addresses the conceptual concerns (and that did so by saying they do not enter the distinctions). I will find answers addressing both the methodological and conceptual portions of my question most satisfying.