I'm not a legal expert but believe the difference is the severity of the crime or if a crime has even been reported. In this case, if the victim told police that there was no crime and a consensual sexual incident occurred, I'm not sure that they would continue to investigate. In hindsight, I'm sure they had investigated further.
PAAM - Victim FAQ
"Many people incorrectly believe that a victim has the power to "press charges" against the wrongdoer, or to later "drop the charges". All crimes are offenses against the community, not just the individual victim. Criminal complaints are prosecuted on behalf of the State of Michigan, not the people who called the police or those who were personally harmed by the defendant's conduct. ONLY the Prosecuting Attorney can issue or dismiss charges. This is important because it takes the responsibility for prosecuting the wrongdoer off the victim's shoulders and puts it on the Prosecuting Attorney's, where it legally belongs. It also means that the defendant cannot "pressure" the victim into dropping the charges.
Although the decision whether to prosecute or not prosecute is ultimately up to the Prosecuting Attorney, the victim's opinion is important and the Prosecuting Attorney will take those wishes into account when making his or her decisions regarding the case. A variety of factors are taken into account when deciding whether to honor a complainant's request not to proceed with a prosecution, including the nature and extent of the defendant's prior criminal history, the severity of the alleged crime, whether the defendant has other pending charges in the criminal justice system, and future danger the defendant poses to the community (including the current victim)."
