Whether or not it's important to you depends on your use. Definitions vary, but these days a full tang runs the length of the knife and is usually visible around the handles. But this same visible tang could also be skeletonized and it is usually done for weight reduction and to achieve the balance the maker wants. For me, I have no issue with skeletonized tangs, but I would like to know just how skeletonized they are since the tang is usually not visible. All that said, for my normal needs, it makes little difference as long as the knife doesn't break with a modest impact such as batoning small wood for kindling. I seldom baton a knife anyway.
Stick tangs are full length tangs where the handle encloses it and the handle is often secured with some sort of nut on the end of the handle. Steel reduction is done to fit the handle over the tang.