Residence by Investment is not the same as Citizenship by Investment. Numerous countries will grant residence to those who invest money in their country, but they do not guarantee that the resident will obtain citizenship because of that donation. All that the investment grants is entrance into the country.
Countries have various criteria that an individual can meet to qualify for a residence permit, from having a job offer to starting a company to marrying one of their citizens. Some countries decide to add an extra option and allow those who make an investment to reside in the country as well without having to meet the other criteria.
Once they are a resident, they can be naturalized the same as everyone else.