Truth and Reality : I have a theory that cultures have a preference for either of them. This can easily be found in their preferred word of choice in the sentence “Did he really/truly do that ?". English prefers Reality (although “truly” is not unheard of), French prefers Truth ("Il a vraiment fait ça ?"). Spanish is in reality’s camp (realmente) as Portuguese. Finnish, Italian, Chinese and Indonesian use Truth. Russian uses a mixture of both, Japanese also, with the added idea of authenticity. Here is a crude map of the matter. Can you add to it ?

Respectfully, I think this is a case of 'folk linguistics' which doesn't reflect any existing, meaningful difference between cultures. I doubt you would be able to find any evidence that either group would perceive the world differently from the other, purely based on an unconscious etymological distinction. In my experience with french, "vraiment" is essentially just used as "really" is used in english. I don't think they are especially distinct.
What would you actually need to prove that it doesn't reflect any meaningful difference between cultures?
If you were to do it semi-scientifically (just to demonstrate), you could test the two groups on an alternate measure that compared their preference for 'truth' or 'reality'. This could be operationalised perhaps by having participants listen to a story then have them answer questions afterwards that test whether they have a greater preference for 'true' details or 'real' details. Then you could compare the groups to see if they are statistically significantly different. Alternatively, you could try a form of qualitative analysis of say newspapers where you critically examine whether they tend to focus on 'true' or 'real' details. How someone would go about it in a different way, e.g. philosophically, is something I don't really know. Language on the whole tends to be quite arbitrary so it is dangerous to read too literally into the meaning of words. To show this in a kind of funny way - the word in many Slavic, Celtic, and Baltic languages for ladybird is "God's little cow". Based on this difference, I could presume that Russian speakers and English speakers perceive the world in two vastly different ways. But in reality it is just a name that speakers will employ without remembering anything of its origin or thinking of its literal meaning.
I will say though that I have never thought about the difference and it is interesting, so I appreciate you bringing it up! A preference between the two may very well exist between cultures. You just will have to find a more solid basis to define it - and I imagine if you do, you will likely see the 'borders' change.