Residency is temporary permission to live in the country. A residence permit is valid for 1—5 years, and then it may be renewed.
Work, study, marriage and other purposes of living in the country lead to residency. Also, it may be obtained by investment, and the conditions will be pretty mild in that case. For example, investors are not obliged to pass any exams or live in the country to maintain residency.
Citizenship implies that a person has full rights and obligations to the state. The status is life-long and is usually confirmed with a passport. Citizenship allows:
to live in the country;
to use all state benefits, for example, free healthcare or education;
to be protected by the state when abroad;
to enjoy visa-free travelling to countries with visa waiver agreements with the state of citizenship.