EDIT: I realized I completely misread the question. I thought it was asking the difference of using a WHERE clause or putting conditionals in the JOIN (see my reply above for an example). The original SO questions is about an old-school CROSS JOIN `table1,table2` (which is a cartesian product in relational algebra) and a JOIN.
Edit 2: "old school" in the sense of joining tables before JOINs existed. I think it was System R the first engine to introduce efficient JOINs vs cross products.