Citizenship by investment programs do not require the applicant to move to that country to obtain or keep the citizenship, and the citizenship certificate and passport are granted in approximately 4 to 6 months.
How long it takes depend on each program and also on the complexity of each applicant’s profile.
On the other hand, Residency by investment programs issue a residency permit (not the citizenship). The process is also fast and within 3 to 4 months the applicant is granted the residency permit and is able to move to that country immediately. However, if the applicant does not want to reside in the country, then there is no need to do so, neither to obtain the residency nor to renew it.
After 5 years minimum the applicant could potentially apply for the citizenship if they have complied with all the requirements by law. The requirements to obtain citizenship vary from country to country.