Irony and paradox are two forms of literature that are actually different in meanings and the way they are being used. Irony can be defined as a statement that is different in meaning or even opposite in meaning compared to what was being said originally. Irony is usually used in a humorous context, expressing the opposite of what you actually mean, or your literal intention.
Literal irony, verbal irony, and situational irony are the three types of irony that we have. An example of irony is "the boy is fast, just like tortoise". Paradox, on the other hand, simply refers to a statement which defies intuition even as it tends to seemingly contradict the said statement.
Another definition of paradox goes thus; a statement which is self contradictory, and can only be false if it is true, or that can only be true of it is false. An example of paradox is "this sentence is false".