The other charges were dropped as part of a plea bargain.
"The film-maker was arrested and charged with a string of offences, eventually admitting to having sex with a minor. The other charges were dropped as part of a plea bargain." http://www.bbc.com/news/world-europe-34679695
He did not serve time under the plea bargain. He was awaiting sentencing although he had been in prison and undergone psych evaluation.
"He spent 42 days undergoing psychiatric evaluation in prison, but was permitted to travel overseas when this was completed.
Polanski's lawyers have said that private conversations with the judge led them to believe that the prison time would serve as his punishment.
However, when it was later suggested that he could return to prison, Polanski decided to flee ahead of sentencing
That sentence is still outstanding and I'm surprised that the US couldn't make their case for extradition. He is a fugitive from justice and has got away with it for nearly 40 years.