Trite comes from the Latin word "tritus", which means "worn out" or "rubbed smooth". This meaning is directly related to the concept of "trite" - something that is overused, commonplace, and lacking originality, as if it has been rubbed smooth by repeated use.
Tritus is a less common word in English, but it can still be found in some contexts. For example, you might see it in a geological context, referring to rock that has been eroded and smoothed by water or wind.
So, while the two words have a shared root, the meanings have diverged over time. "Tritus" refers to a physical state of being worn out, while "trite" refers to a metaphorical state of being worn out, specifically in terms of language and ideas.