"They are stopping production" would probably be a more natural translation.
Agreed. I said "they're stopping manufacturing," which should also be accepted.
I get the sense that לעצור is more along the lines of physical stopping, whereas להפסיק is more like we might say colloquially where I come from (in Canada) to "quit" doing something. For instance, you can "quit" bothering someone and "quit" working (for the day, or on a break). Whereas you wouldn't "quit" your car at the intersection, you'd "stop" it, because it's more of a physical thing. Another thought: if you think of הפסקה as taking a break, you'd probably use להפסיק (same shoresh and binyan) anytime you're taking a short break. In this case, if this sentence above said הם מפסיקים לייצור, instead of עוצרים, I might assume that production was going to be resumed at some point, they were just on a break, whereas this sounds to me as if it's finished for good. I hope some of that makes sense... I have no grammatical training, just speak, read, and write Hebrew a lot these days. :-)