No, simply look at the product page - driver subpage - and you will discover that the two products use different drivers.

Sorry I can't give you a link because the location is scripted, you need to look it up on your own.

You need to install both ASIO drivers, one for the UFX II and the other for the BBF Pro.

Wondering about your question. Didn't you install the RME driver already for the BBF Pro ?
Same  procedure for the UFX II. Its simply a different HW/design which requires the newer USB driver.

BTW .. an ASIO driver can't come from Microsoft. Its a speciel driver that comes from the vendor who designed / build the recording interfaces, as ASIO driver are high performance / low latency drivers directly accessing the hardware of the recoding interface. Thats the clue .. it doesn't have to go through Windows sound system which is laggy and not high quality in every aspect.

With the new webserver its even easier to identify the proper driver. Simply open UFX II product page, it has a subpage "Drivers", download and install.

Many thanks, you're welcome

> I wondered why it said Fireface USB Settings and not "Babyface Pro USB Settings"

Because this message is only related to the driver name not to the devices that you may connect.

driver_usb_win_1168 supports
---> Fireface UFX - UCX - 802 - UC, Babyface, Babyface Pro

driver_madiface_win_09685 supports
---> Fireface UFX+/UFX II, MADIface XT/Pro/USB, OctaMic XTC, ADI-2 Pro/AE/FS/DAC, Digiface USB

> I wondered why it said Fireface USB Settings and not "Babyface Pro USB Settings".
> Furthermore, when I open the USB Settings icon and the menu is displayed it reads at the very top "Fireface"
> and then below that it reads Babyface Pro (1).

Same reason as above. One message is related to the driver, "Fireface" USB driver, the other one then finally shows the detected devices...

> How can I show you pictures/ screenshots?

Many people like Greenshot as screenshot tool and Dropbox as Cloud Storage.
Install Dropbox, create an account for you etc ...
After the Dropbox installation store the screenshot to your disk.
Click with right mousebutton to the screenshot the you can
- move the file to the dropbox and
- share the file
By sharing a link is created.
This URL you paste into a posting on RME forum.
Change the end of the URL from "....dl=0" to "....dl=1".
Enclose this URL by image tags to indicate this is a picture to be displayed.
"[img]xxxxURLxxx?dl=1[/img]"
dl=1 ensures that the browser should load the file directly when displaying the page so that the user does not need to click anything to see the picture.