Depending on the requirements of a geometer, you can use the Zariski / etale / syntomic / etc. Topology on the spaces they are looking at. I know some settings where the etale topology is better suited for the task than the Zariski topology and where the fppf or fpqc topology is better than the etale topology. However, I do not know any situation where the fppf topology is better than fpqc or vice versa. Do such situations occur in algebraic geometry?