In some states drivers who are arrested for drunk driving may be charged with a DWI or driving while impaired. Some states may also differentiate between DWI (driving while impaired) and DUI (driving under the influence), which can be a lesser charge. In these states a driver may be arrested for drunk driving but may be able to plead their DWI charge down to a DUI charge if their blood alcohol level is below a certain limit at the time of the arrest, they are a first time offender, and they show remorse for their actions.
A law enforcement officer may arrest a driver for Driving While Intoxicated (DWI), Under the Influence (DUI) or Operating [a motor vehicle] While Intoxicated (OWI). Which term is used depends on the individual state, but each of the three terms means basically the same thing. An officer makes the determination that a driver is drunk based on observations of the driver.
These are just a few signs a police officer may see to help in determining if you are drunk driving or not.