It's difficult to know precisely without context but there are few cases where this could be relevant, in particular:
- Travel documents other than passports (e.g. refugee travel documents) are issued by the country where the person resides and indicate that the holder can be readmitted to the country of issue even though they are still citizens of another country. Formally, these documents are typically not called “passports” but they look like one and are often informally called “refugee passports”.
- Some countries like the UK and the US have a distinction between “citizens” and “nationals”. For the US, some people from the American Samoa can for example get a passport issued by the US Department of State but cannot claim the US as their “country of citizenship”.
- People living in countries that are not recognized as such by many other countries in the world (e.g. Palestine, Northern Cyprus) sometimes travel with a passport from another country (e.g. Jordan, Turkey) where they might or might not be considered a citizen. However, it would be difficult to accept “Palestine” as “country of citizenship” if it's not officially recognized wherever you are so that's probably not the intent of the form.
On the other hand, if you have a regular passport, issued by your country's authorities, then I would tend to think that “country of issue” and “country of citizenship” are the same even if you got your passport through a consulate abroad (that's certainly the terminology used by the US authorities, as shown in the link provided by Mark).