The resident permit and long-term visas are valid as far as the free movement of the person in the Schengen Area is concerned. Any citizen who holds a long-term visa (such as the resident permits for real estate owners) that has been issued by a member state is able to travel to other member states for up to three months within a six-month period. This is under the same conditions that apply to the holder of a resident permit while they are also granted the right for multiple entries. The period of three months is totally considered not for every country.
What are the traveling requirements to the Schengen Area if I have a Greek residency permit?
I understand that if receive a Greek residency permit, I am entitled to freely travel to other Schengen countries for a period of up to 90 days within any six-month period. Does the stay restriction apply to the whole Schengen Area or just one certain country? For instance, if I need to travel to Germany and France during a six-month period, can I stay 50 days in Germany and another 50 days in France (which would make it 100 days in total in Schengen Area, but not exceeding the 90-day limit for each country)? Or does the combined stay have to be, at most, 90 days?
Once you have the resident permit you can travel freely in the Schengen Area as if you had a visa. So you are right: This means that you can stay in other Schengen countries for 90 days within any six-month period. This applies to the whole area. You can stay, at the most, for 90 days. For example, 50 in Germany and 40 in France, but not 50 and 50 in each.
You can stay as long as a European citizen can. So 90 days in each Schengen country (e.g., 50 plus 50 plus 50 in every different country).