【Fallacy】 , 【sophism】 ,  【sophistry】 ,  【casuistry】  are comparable when meaning unsound and misleading reasoning or line of argument.

The same distinctions in implications and connotations are distinguishable in the corresponding adjectives fallacious, sophistical, casuistical.

【Fallacy】  and fallacious in specific logical use imply an error or flaw in reasoning that vitiates an entire argument; thus, a syllogism in which one argues from some accidental character as though it were essential and necessary (as, The food you buy, you eat; you buy raw meat; therefore you eat raw meat) contains a  【fallacy】  or is fallacious.

In more general use  【fallacy】  and fallacious apply to a conception, belief, or theory that is erroneous and logically untenable, whether it has been arrived at by reasoning or by conjecture or has been taken over from others.

【Sophism】  and  【sophistry】  and sophistical imply, as  【fallacy】  and fallacious do not necessarily imply, either the intent to mislead or deceive by fallacious arguments or indifference to the correctness of one’s reasoning provided one’s words carry conviction; the terms, therefore, often connote confusingly subtle, equivocal, or specious reasoning.  【Sophism】 , however, applies usually to a specific argument of this character,  【sophistry】 often to the type of reasoning employing sophisms.

【Casuistry】  and casuistical imply 【sophistry】 only in their extended senses. In their basic senses both have reference to the science that deals with cases of conscience, or the determination of what is right and wrong in particular cases where there is justifiable uncertainty.

In their extended use both terms usually imply sophistical and often tortuous reasoning in reference to moral, theological, and legal problems.