You can buy the adaptor brackets to go with or without a tow bar, so a tow bar is not necessary at all. I accidentally ordered the ones to go with a tow bar, and when I realised my mistake, I ordered (& fitted) a tow bar as well (which has actually turned out to be useful for carrying bicycles) even though I was not intending to get one.
However, I can't tell what the difference might be? The adaptor plates mount outside the tow bar brackets, so they might be that thickness further apart I suppose. But that difference shouldn't affect the overall system.
To fit the brackets to mine, I had to cut the welded-on nuts off the tow bar mount (the part that fits to the chassis rails). This is because the Cate brackets are themselves threaded and fit flush on the outside of the tow bar mounts. I would imagine that this aspect would be similar for a removable swan neck tow bar.