No I have the same structure under Daz Studio Formats as the image below shows.
Ok some history for you. DAZ originated as a division of Zygote Media Group, Inc. creating content for the application Poser. In December 2000, DAZ branched off from Zygote, and became a freestanding corporation (source http://en.wikipedia.org/wiki/DAZ_3D) and with that came the rights to use Poser formats hence the cross compatibility.
With some products you need to install both files, Poser and Daz Studio which is the case for Cliffhanger. Poser files contain the geometry CR2 or PP2 and poser materials PZ2 or MC6 whereas the Daz Studio file contains the Daz Studio material presets .ds.dsb, dsa etc. This is because Poser and Daz Studio have slighting different ways it handles surfaces mainly Glossiness.
Some content is Daz Studio specific, like shaders etc so they will only have Daz Studio formats.
Some content have Daz Studio material presets taht show up in the Poser Format directory even though they are Daz Studio material presets. Yhese have a special script (code) Eventually you will come across these. See the small image below.
A general rule of thumb is that if both the Poser and Daz studio files are of equal file size, or thereabouts, then you only need to install the Daz Studio formats. But since I use Poser too I install the lot just to make sure.
If you aren’t sure install the daz Studio only file, start up Daz Studio and take a look. You can always install the Poser files after. 
You can remove the content manually from your Hard Drive if the uninstaller failed, why it failed I cannot say, sorry.
Yes it is confusing and you are not alone. Took me a good few months of reading before I got my head around it all.

Click thumbnail to see full-size image