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.