For the most part, the police can charge you with anything they want. They have great discretion in who they charge with what.
Typically, the arresting officer will file the original charge. A superior police officer may change the charge after reviewing it, or the prosecuting attorney might decide to charge a different offense based upon the facts of the case. Sometimes this can work in your favor, and sometimes this may work against you.
Contact a local criminal defense attorney for more specific information.
Yes. Police will charge you with what they believe to be the relevant offense. It is, however, the prosecutors who decide which charges to proceed to trial on.
While people (including police officers) often confuse the terms, there are three different forms of "drunk driving" in Washington, D.C.: driving while intoxicated (DWI), driving while under the influence (DUI), and operating while impaired (OWI). All three forms require the prosecution to prove that the defendant "operated" or was in "physical control" of the vehicle. Where they differ is with respect to the second element of the offense: impaired driving through intoxication.
Generally speaking, the prosecution will proceed with a DWI when it is in possession of a chemical test showing that the person's blood alcohol concentration was above the legal limit. Assuming that the prosecution is able to introduce this test, intoxication will be presumed. DWI only covers alcohol.
DUI covers both drugs and alcohol. As with DWI, the prosecution must still make out operation/physical control. In addition, without results from the chemical test, the prosecution must make out impaired driving ability as a result of drug or alcohol consumption.
Finally, under OWI, a person can be prosecuted with any amount of drugs or alcohol in his/her system if the prosecution can prove that the consumption impaired his/her driving ability. While this is an easier case for the prosecution to prove, there are also lighter penalties associated with this offense.
While I cannot say for sure why you were stopped for one offense, cited for another, and then charged with the original offense, I imagine the police officers may have been using the terms DUI and DWI interchangeably when they first stopped you. The prosecutors then looked at the facts of the case and decided to proceed with the DUI.