Battery cable replacement

Sounds like this smaller wire that is capped is a redundant ground which is pretty common.

I am attaching the process from the manual on the negative cable plus a picture of what the cable should look like.

Can you attach a couple pictures of what you are looking at just so we can be sure to be on the same page?

However, if the car runs then clearly the cable is working but we need to confirm that the replacement is the same as the one that is removed. If they are the same then clearly each connection needs to go on in the same place.

The fact that you are seeing something different on the replacement cable makes me think it is not the right part.

Let's start with this and go from there. Thanks