A primary election is an election during which voters can indicate their preferred candidate in an upcoming general election. In other words its a process for narrowing the number of candidates for general elections.
General Election is a process, during which, nation's primary legislative candidates a nation or state are elected. Generally they are held at some intervals such as every four years.
Special Election is an election scheduled at unusual date for a specific purpose. It happens generally to fill an position that has become vacant before the incumbent has completed the term.
Run-off Election means an initial election did not result in a winner because it was tied or too close to call. A runoff election settles the matter, providing a final decision.
A Recall Election (is also known as recall referendum and it is a procedure when voters elected official can be removed from the post via direct vote before that official's term has ended.