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.
Limitations on running for reelection to an upper house, such as a Senate, often include term limits set by state or federal laws, which can restrict the number of consecutive terms a candidate can serve. Additionally, some jurisdictions may impose age or residency requirements, and candidates may face restrictions based on previous conduct or legal issues. Political party rules and primary elections can also limit a candidate's ability to run for reelection, as they may need to secure party nomination to be on the ballot.
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.
giving journalists access to research data supporting a party position and creating a website listing the accomplishments of party candidates up for reelection
The mayor who is in office and running for reelection.
The incumbent, Gerald R. Ford, ran for another term in 1976. Bob Dole was his running mate.