Cuba does not have two presidents in the sense the term is usually understood. Off my head I cannot think of any country that does.
Cuba has one head of state, the president of the Council of State, which as of this writing is Raul Castro. In countries with a parliament, it is not uncommon to elect or name one person to be the head of this body (off my head, I cannot think of one that does not). This title for this role may differ, e.g. "speaker" (UK House of Commons / House of Lords, U.S. House of Representatives) or "president" (see also "President pro tempore" of the U.S. Senate).
Using the latter title in no way implies that the holder of this office has the same or similar role as the president of a country. Germany, for example, has a "Bundespräsident", who is the (figure-)head of the federal state, a "Bundestagspräsident" elected by the members of the lower house (Bundestag) usually for its whole term. Then each of the 16 states' governments is lead by a "Ministerpräsident", on of which also heads the states' representative body and thus is also "Bundesratspräsident" (rotating, changing every 6 months), who may also fill in for the actual Bundespräsident shall he (always he, so far) be incapable or the office be vacant.
Summing up, the constitution of each country usually defines who is the head of state and who is the head of government, whether these are different offices at all and whether any of them shall be called "president". This in no way prevents other institutions to have an office also named president.
As for "How do their powers differ?": Obviously, one heads the government and one the pariament. The actual powers in the case of Cuba are enumerated (like in most countries, I suspect) in the constitution; see especially articles 81 and 93.