One of the fundamental characteristics of human cognition -- perhaps the most fundamental characteristic -- is the strategy of comparing an X and a Y (where X and Y may be entities, states, processes, concepts, ...) to identify the ways in which they are distinct and the ways in which they are the same. Both the differences and similarities are also fundamental to research in all academic domains of inquiry, where 'similarity / sameness' been abstracted away as the equivalence relation, algebraically expressed as 'X = Y' , which means "the quantitative value of X is equal to the quantitative value of Y along the dimension of comparison D." The qualitative part of the equivalence relation is the bidirectional implication expressed algebraically as 'X <--> Y in formal logic.
You can read the entire article here. The write up is on the manifestations of (and terminologies for) the equivalence relation across domains of inquiry. It takes examples from Geometry, Biology and Linguistics. I hope that a subset of researchers and research students I am sharing this with would find the contents of the document interesting. Needless to say, I would be happy to receive feedback on this document (in terms of (dis)agreements, objections, corrections, suggestions for improvement and further thoughts.