1, with different meanings: fallacy is a statement that does not conform to logical thinking and an assertion that needs logical refutation. Fallacy usually refers to the proposition that the reasoning process is wrong and the concept is stolen. Paradox refers to the conclusion that can't be obtained in reality when the contradictory hypothesis is taken as an optional branch in logic. Paradox starts from a seemingly reasonable premise and deduces a contradiction through seemingly reasonable logical reasoning.
2. Different forms: fallacy is a statement that does not conform to logical thinking, and it is an assertion that logic wants to refute. Paradox is not. Paradox refers to the conclusion that is impossible in reality because of using contradictory assumptions as substitutes in logic. The paradox of set in mathematics is caused by the too broad definition of set and the contradictory items being added to the same set.