I've created wiki excerpts for both the floor and flooring tags; the "floor" tag is awaiting peer review. Currently as stated, these tags differentiate based on whether the question relates to design, materials and construction of the structure of a floor, or to the materials and installation of floor coverings aka flooring. However, this seems a pretty thin line for a topic in which both sides are usually addressed, so I thought I'd put it up for discussion as to whether one tag should be a synonym of another, or any other possible change to the tag such as renaming "flooring" to "floor-covering" etc.
Please keep them separate. As you stated, there is a real difference between "floors" and "flooring" and knowledge of one does not necessarily mean knowledge of the other.
Keeping the tags separate is also indispensable for search. "Floor" and "flooring" are both such generic and common terms that ordinary searches are useless (and will get exponentially more so as the site grows).
It should be clear that tags are indispensable in power-searching for otherwise generic terms. Please do not merge these two tags.