Mark, short stay or tourist visa requirements are set by the Schengen group of countries as a whole on a consistent basis ie what is agreed by one is agreed by all.
https://ec.europa.eu/home-affairs/what-we-do/policies/borders-and-visas/visa-policy/schengen_visa_en
For tourists wanting to travel long term in Europe this results in the “Schengen Shuffle” where you spend 90 days ‘in’ and then 90 days ‘out’ of the Schengen countries. The 90 day requirement is based in large part on the principal of reciprocity between countries. The US, Canada and other countries only give Europeans a 90 day tourist visa. It’s a kind of ‘you get what you give’ between nations.
Immigration requirements and long term residency rules are set by each individual country. If you want to stay longer than 90 days in a country you have to apply for some type of long term visa, a work visa, a retirement visa etc. Each country sets their own rules. You can obtain a permanent residency card in Greece by buying property there (subject to a number of other requirements) and this allows you to reside for as long as you like in Greece. As a resident of any Schengen country you can visit any other country - you must carry your passport and your residency card. Unless you have an EU passport, you are still subject to the 90 day limit in any country.
As long term residency/immigration is a national affair, you cannot ‘purchase’ a Greek residency and then go and live in France. For immigration and residency requirements you need to search by country as each is a little bit different, ie France’s requirements are extremely bureaucratic and pedantic, while Belgium is a little more relaxed. Requirements vary by both the country you want to reside in and by the passport you hold.
https://france-visas.gouv.fr/web/france-visas/long-stay-visa
If you have a PASSPORT from any EU member country, ie you are a citizen of an EU member country, you can move to and live in any other member state at will. You are still required to register your stay with that country for social insurance and health care purposes etc. but you have the right of free movement within the EU.
A residency permit DOES NOT give you the same rights as a PASSPORT.
Visa requirements, whether short term or long term are based on your passport, not your residency.