It means that the balance point-the spot on the shaft where the racquet will be evenly balanced-is somewhere between 280-295mm or 290-300mm from the butt end, on a blank racquet without strings or clingwrap. Yes, without clingwrap. The figures you give of a 10mm-15mm range represents very poor quality control at the finishing department. The tolerances should be +/-2mm for badminton racquets and +/- 5mm for tennis racquets. In badminton racquets, the finishing department uses a wooden hold of the appropriate weight and/or silicone/lead counterweight to balance a racquet's b/p to its designed b/p. Hence its tight tolerance of +/-1mm to 2mm. In tennis racquets, no such balance point qc step is done, hence all the tennis racquets of one designed end up with a wider tolerance of +/-5mm.
Am I correct to say that a racquet that says "300mm" is heavy headed, while a racquet with say "280mm" is headlight?
Not necessarily, but with the same design the longer b/p racquet will be more head heavy or conversely the shorter b/p racquet will be more head light, relative to each other. This applies to the same design and model. Some racquets with 300mm b/p do not feel head heavy at all. The terms head heavy and head light are used by some to describe the feel of the racquet. There are others who use the terms attack and defence, anything over 295mm for attack and anything less than 295mm for defence. There are also others who use the term even balanced, which is in between head heavy and head light.
If I were to reduce the wooden grip of the racket, does it make the head light racket a head heavy one? Thanks.
Any weight you take away from the handle end will make your racquet head heavy. As a matter of fact you can do a simple calculation first to decide how many mm you want your racquet's b/p to move higher instead of the usual trial and error method. But why would you want to change your racquet's b/p from its designed b/p? Usually making a racquet more head heavy will increase its power for high shots, like smashes and clears, but will decrease its power for low shots like full length return of smashes and drives/flicks. You can also make your racquet more head heavy without reducing any weight on the handle, and that is to use a little-not more than 0.5g-lead tape on the frame top. But this will also have plus and negative power changes. Also, the increased air resistance caused by the lead tape at the most critical spot will slow down the speed of your racquet.