It is never a good idea to translate word-for-word. Different languages have different rules. You translate by usage. Context is everything. Register makes a difference.
"Mulțumesc" is used politely/formally. The equivalent in English is "thank you".
"Mersi" is used informally. The equivalent in English is "thanks".
I've seen several well-educated native speakers who did not consider "mersi" a Romanian word. They asumed it's simply "merci" from French (just like how people would sometimes throw you a "danke" or "thanks"). But the word is in our most official dictionaries with an adapted Romanian spelling.
For what it's worth, I'm from Bucharest and I use "mersi" almost exclusively (using "mulțumesc" only when I want to be very polite).
This is telling me this is only 'thank you' and not 'thanks'. There is not a difference between them in English usage. The shades of meaning discussed here are not present in the English expressions. 'You' does not make 'thank you' more polite than 'thanks'. As a result, I think they should both be accepted and the shades of meaning can be left for places like this or notes.
The difference in English usage isn't necessarily one of meaning, but one of register: https://en.wikipedia.org/wiki/Register_(sociolinguistics)
An American or British English speaker would never say "thanks" in a formal setting, for example. In Romanian, the difference between using tu and dumneavostra is one of register, not meaning. In the same way, the difference between multumesc and mersi is one of register and relevant here.