A Citizen belongs to a certain country, whereas a resident is permitted to live there having met certain conditions. The most notable difference is citizenship allows one to apply for a passport for the country in which one resides.
Citizenship holds more rights than a residency permit or visa, like for example the right to vote. Residency is also less permanent and requires renewal after certain time periods. Residency does however often allows entrance to the country at any time, purchase of property, access to health insurance, and enroll your children in school.