Here's a definition of both.
You will note the power lies with the people in both counts through elections.
Both are democracies but different heads of state.
You do not know what fascism or banana republicanism means. You are an ignorant fool.
Republic: "A state in which supreme power is held by the people and their elected representatives, and which has an elected or nominated president rather than a monarch." Democracy: "A system of government by the whole population or all the eligible members of a state, typically through elected representatives."