It is widely established that there are some nonhuman animals (like Great Apes and some bird species) capable of folk psychology, which is usually defined as attribution of mental states by one animal onto another animal. However, this capacity is sometimes thought to be synonymous with the capacity for metarepresentation, which is usually defined as the representation of representation qua representation. But the latter capacity is a more advanced version of the former capacity. Why? Because it is erroneously assumed that the only kind of folk psychology is internal psychology whereby the attributor represents the other animal as having some unobservable internal representation inside their head. However, just as behavioral psychology historically preceded cognitive psychology, it seems plausible that, phylogenetically, behavioral folk psychology preceded cognitive folk psychology. That is to say, before humans ever started representing other humans as having unobservable but causally efficacious mental states in their head, we merely represented their behavior in our minds as confirming to some particular schema. Thus, the computational form of behavioral folk psychology would be something like “Conspecific A behaved like X in the past, therefore Conspecific A will likely behave like X in the future”, whereas the form of a cognitive folk psychology would be something like “Conspecific A believes X, desires Y, therefore Conspecific A will act like Z in the future”, with belief and desire understood explicitly to be some unobservable mental event.
With that said, it becomes easy to see why we should distinguish the capacity for folk psychology from the capacity for metarepresentation. Only creatures capable of cognitive folk psychology can metarepresent. But don’t be fooled. The capacity for behavioral folk psychology can get you a very long way in terms of executing complex chains of social reasoning. This likely explains the depth and sophistication of nonhuman social cognition. But I am aware of no evidence that compels us to believe any nonhuman species is capable of human-esque metarepresentation, which, imo, stems from our mastery of language, particularly linguistic concepts that have to do with psychology such as the terms “belief”, “desire”, “mind”, soul”, “consciousness”, “intention”, “thought”, “dream”, “reason”, etc.