Pretend somebody committed two different acts that were considered crimes in their country. This person then fled to another country, where only one of their acts is considered a crime.
In the above example situation, would an extradition be allowed to bring the offender back to their home country? Would there perhaps be some type of agreement between the two countries to only punish the offender for the act which was considered a crime in both jurisdictions, and to drop the other charge?
I ask this question in general, rather than for a specific country overview. It might be easier to avoid United States law as it tends to get complicated.