Very theoretically example. Bank robberies are illegal virtually everywhere. At least that's my assumption.
But in principle you're correct.
If Bob commits a crime in country Ypso and flies home to country Zorg then Zorg will only extradite him if the crime he committed is also a crime in Zorg.
As a more practical example: Switzerland makes a distinction between tax evasion (which is not a crime, but a misdemeanor) and tax fraud, which is a crime. The difference is that when you "forget" to declare income this is tax evasion (to a degree), while if you cook the books that's tax fraud. Most countries don't make this distinction.
Switzerland got a lot of heat for neither providing information, nor extraditing people accused of tax evasion to another country. The reason being that it's not a crime in Switzerland.
Practically, that doesn't really matter much any more due to the whole information exchange on tax issues, which the country is also part of.
There are other reasons for not extraditing a person. For example if such a person is a citizen in a country that doesn't extradite its citizens then any extradition request from another country will be denied.
