I was in parts at a CAT dealer for a few years and understand the importance of correct machine ID. It was the same for medium duty GM trucks. If you didn't have the line sheets finding the right part was just a guess. VERY difficult to convince customers that no, "they are not all the same". Even the mechanics needed a refresher course from time to time. I have never encountered CAT using the same number for different parts.I have seen this on Cat and Detroit parts as well as on my dozer. On Cat parts it will go by arrangement number, on Detroits it goes by the spec label/tag on the valve cover or generator label. Falk marine gears and clutches are similar. It's a big-ass headache too because sometimes there is a part number change with no change in the part. This is all to keep trade secrets and competition on their toes (and job security for others). So it's really important to include year, make, model, and serial number(s) of the machine for any part you're ordering.
True story: When I was a marine engine dealer in the '70's I would get calls for parts for a "blue" engine. After awhile it ceased being funny.
Our biggest headache is we had farm equipment too. Every time a manufacturer sold or consolidated, the new corporation in charge issued new part numbers and sometimes tried to consolidate the total number down. But if you looked up a Farmall bearing and the book said #123 what you didn't have any way to know that Massey had changed that number to 567 and there were 3 on the shelf that would work just fine. Bad situation for the dealer and the customer.
Then there was the opposite where a manufacturer would make machines for another brand, kind of like our situation with Jinma making all kinds of brands. I remember ordering a shaft for a baler that the guy swore up and down was a Heston. The part didn't fit. Ordered another, same thing. Finally convinced the customer to bring in the old part. Called tech support with calipers in hand. Spent a lot of time trying to figure it out. When tech support asked for the machine serial # the customer got really testy about it. Of course he had repeated "they are all the same" so many times we thought about getting him license plates that said that. Come to find out, he had a Case bailer (made by Heston) but several of the parts were spec'ed differently for Case. This was a Case only part and obsolete. I called the Case dealer and confirmed that the customer had been there and knew that but still put our dealership through hell even though we couldn't get the part for him. (the names and numbers above were changed to protect the innocent)