【Caprice】 , 【freak】 , 【fancy】 , 【whim】 , 【whimsy】 , 【conceit】 , 【vagary】 ,  【crotchet】 are comparable when denoting an arbitrary notion that usually lacks a logical basis and therefore may be unsound, impractical, or even irrational.

【Caprice】 emphasizes the lack of apparent motivation and implies a certain willfulness or wantonness.

【Freak】 suggests an impulsive, seemingly causeless change of mind, like that of a child or a lunatic.

【Fancy】 stresses casualness and lack of reflection in forming an idea and may sometimes suggest a kind of harmless perverseness in the idea formed.

【Whim】 and 【whimsy】 suggest not so much a sudden as a quaint, fantastic, or humorous turn or inclination, but 【whim】 often stresses capriciousness, and 【whimsy】 fancifulness.

【Conceit】 suggests more strongly than 【whim】 or 【whimsy】 the quaint, fantastic, or erratic character of the notion formed and also may suggest the firmness and persistence with which it is held.

【Vagary】 suggests still more strongly the erratic, extravagant, or irresponsible character of the notion or 【fancy】 .

【Crotchet】  implies even more perversity of temper or more indifference to right reason than 【vagary】 ; it often is applied to a capriciously heretical opinion on some frequently unimportant or trivial point.