Natural born citizens include people 1) born on U.S. soil (or a U.S. military base 2) born to parents who are U.S. citizens. Only natural-born citizens can become U.S. president.
Naturalized citizens go through the naturalization process. That is usually when a legal permanent resident (Green card) applies for citizenship after a period of time as a legal resident (usually 5 years). The resident will take tests, like U.S. history and government, and eventually be sworn in as a U.S. citizen. That is called Naturalization.
All citizens can vote and serve in every public office except the presidency.
Write-In vote: In many places, if you do not want to vote for any candidate on the ballot, you can “write-in” the name of the person you want to vote for.