Both of these doctrines are about the idea that the United States should be the most important power in the Western Hemisphere. They were issued decades apart, with the second (the Roosevelt Corollary) claiming more power for the US than the first did.
The Monroe Doctrine was announced in 1823. This doctrine was inspired largely by the fact that so many Latin American countries were becoming independent at that time. The doctrine stated that the United States would not tolerate any outside powers coming in and interfering with the newly independent countries. In other words, no European countries should try to recolonize the newly freed countries or otherwise try to take control of them.
The Roosevelt Corollary was set out in 1904. It asserted that the US had the right to intervene in the affairs of Latin American countries if those countries were acting in ways that made it likely that European countries would intervene. For example, if a country in Latin America was defaulting on its debts, the US could go in and take over the country and force it to pay its debts to prevent European countries from coming to try to collect the debts by force.
This second doctrine was more expansive because it claimed that the US had the right to intervene preemptively in the affairs of its Latin neighbors.