【Distinguish】 , 【differentiate】 , 【discriminate】 , 【demarcate】  are synonymous when they mean to point out or mark the differences between things that are or seem to be much alike or closely related.

【Distinguish】 presupposes sources of confusion; the things considered may or may not be alike, but if not alike, they are so closely connected, so indissolubly related, so open to misunderstanding that the differences must be noted or marked out if confusion is to be eradicated; hence, maturity of intellect or of judgment is implicit in the power to 【distinguish】 .

【Differentiate】 implies either the possession of a distinguishing character or characters, or more commonly capacity to ascertain differences between things susceptible of confusion.

【Discriminate】 involves the idea of perception; it implies the power to perceive or discern differences, often slight differences, between things that are very much alike.

【Demarcate】 implies the setting of literal limits or the marking of literal boundaries, but it can be freely used to suggest a distinguishing between things as clear as if there were lines between them.