Rest! It’s a word that’s also part of arrest, and interest, and wrest is probably involved in some way. We also have forest, but since rest is not actually a suffix in that word, it doesn’t count here.
Rest has two main definitions, one meaning sleeping or taking a break, the other a synonym for remaining. Sleep rest comes from the Old English raeste which could mean rest like we know it, bed, or mental calm. It’s prevalent across many Germanic languages, but it’s origins from there are a mystery. However, its Old High German equivalent is rasta, which meant both rest as we know it and “league of miles”, so apparently it also had something to do with distance. What that signifies is anyone’s guess.
There’s also the other rest, the remaining one, if you will. It comes from the Old French rester, to remain, and the classical Latin restare, stand back or be left. The re is actually the prefix re-, which means back in this case. -Stare means to stand, which survives somewhat in the word stet. The reason these two definitions have the same spelling? Coincidence, plain and simple.
We don’t use wrest much these days. It’s frequentative, wrestle, is far more common. Wrest comes from the Old English wraestlan, where it meant twist or wrench, and the Proto Germanic wraistijanan, a version of the word wrig/wreik, to turn. The idea of removing or detaching didn’t show up until the early fourteenth century, while removing by force showed up in the early fifteenth century. It has absolutely nothing to do with any version of the word rest. I’m just posting about it to fill up space.
Arrest showed up in the late fourteenth century, coming from the Old French arester, to stop, and Vulgar Latin arrestare. The prefix ar- is a variation of ad-, which means to or at. The suffix is of course restare, which gave us the remain behind rest, so it’s the verb of to stay behind (writing “to to stay behind” is kind of weird). Basically, it’s making someone stay behind.
Interest as we know it showed up in the early seventeenth century, but it came from an earlier word from the mid fifteenth century that meant a benefit or a legal claim. Interest comes from the Anglo French interesse, legal concern, which itself comes from the Medieval Latin interesse, compensation of loss. See the evolution? Compensation to legal concerns to benefit. But what’s interesting (ahem) is that interesse comes from the classical Latin interesse, which means…interest. It went from the definition we know it as to something different and then by the time it was finally translated into English, it started to go back to the old meaning. You can’t see it, but I’m rolling my eyes right now. Anyway, interesse is a mix of words, in this case inter-, between, and -esse, which means to be. The T is just something we English speakers slapped onto it.
TL;DR: One definition of rest is related to arrest. Any other word with rest in it is just coincidence.
Tony Jebson’s page on the Origins of Old English