Partial cover and concealment are identical to cover and concealment.
It's a confusing terminology change that happened part-way through 4e's lifespan, not the addition of an extra level of cover and concealment. The modifier "partial" was added to 'normal' concealment --probably in a well-meaning effort to clarify things-- and both the Rules Compendium and the Online Compendium parenthetically note that it is "sometimes simply called 'concealment.'" (RC 222)
The Online Compendium's glossary entry on cover still hasn't appended the modifier "partial," nor does it note that this word might sometimes be added, but the Rules Compendium uses the phrase "partial cover" and adds that it is "sometimes simply called 'cover.'" (RC 220)
Keep an eye on "superior" and "total," too.
There is equal potential for confusion in the upper echelons of cover and concealment: better cover is called "superior cover," while excellent concealment is "total concealment." I see no particular reason these two similar effects should have different modifying terms, and am surprised that only one item (the
Nightmare's Keen Senses from DR 393) is currently confused by this (according to a search of the Online Compendium at the time of this post).