incumbent
a person who is running for office is a candidate
senator
He is known as the "incumbent."
Yes, a candidate is someone running for political office
No, they are not. According to IRS Publication 529: Nondeductible Expenses, "You cannot deduct campaign expenses of a candidate for any office, even if the candidate is running for reelection to the office. These include qualification and registration fees for primary elections."
The word candidate is most used when a person is trying to take a role in a higher up position. A person running for chairman or mayor would also be known as a potential candidate.
The word "candidate" can be used as a noun in the present or past tense to refer to someone who is running for a position or applying for a job.
In the world, there are several presidential elections going on this year, but I will assume you are talking about the U.S. Yes, Barack Obama is running for reelection.
The mayor who is in office and running for reelection.
giving journalists access to research data supporting a party position and creating a website listing the accomplishments of party candidates up for reelection
The incumbent, Gerald R. Ford, ran for another term in 1976. Bob Dole was his running mate.
A politician who is running for public office is a candidate.