Collocations are probabilities, Cyborg, they are not legislated. Although rich country is more likely than wealthy country, I suspect that both are used with some frequency. Let’s check with Ms Google, shall we?–
781,000 English pages for “rich country”
165,000 English pages for “rich nation”
140,000 English pages for “wealthy country”
84,300 English pages for “wealthy nation”
27,900 English pages for “affluent country”.
13,800 English pages for “affluent nation”.
As you can see, all these collocations are in use, and frequency is on a gradient. There are no rules about, for instance, which adjectives can be used with which nouns; people simply tend to hear them one way and repeat them-- it makes communication quicker when we speak in chunks rather than single words.