"I see so many different claims and labels of honey in the shop. What does the term "pure honey" actually mean?"
"Pure honey" can be taken to mean "100% unadulterated honey with no other contents (for instance, water, sucrose) added", or at least this would be what I think honey suppliers would hope how consumers read. However, to be on the critical side, I would not rule out the possibility that "pure honey" simply means "real honey" and thus the product may contain "real honey" in an unknown amount not necessarily equivalent to 100%. Whatever it is, the term "pure honey" can be ambiguous and even misleading.
Can I assume that "natural honey" means "unpasteurized honey"?
I don't think so. While honey retailers may wish that consumers would associate or even equate the "natural honey" label with meanings of "unpasteurized honey" or "raw honey", the fact is the "natural" label on honey does not render it any more special than other honey. Most commercial honey, even those labelled as "natural" is filtered and pasteurized or treated with heat to slow down the process of crystallisation so that they remain smooth and presentable on the shelves.
(Ironically, sparkling and speckle-free honey is somewhat perceived by consumers as good quality honey.)Unpasteurized honey is now mostly directly purchased from the local honey farms, which do not exist in places within easy reach for some consumers. Every country has its own regulations regarding the "pasteurized" labelling; for some countries, the term "unpasteurized" label on honey is prohibited, but you can find the label "raw" instead.
Since cream honey appears more concentrated, is it then better than liquid honey?
Form is not a factor in judging the nutritional value of honey. Cream honey, which is formed by allowing the honey to granulate at a controlled temperature of about 55 degree F., can be better in terms of convenience for some consumers who find it less messy to spread the honey over toast or biscuit, whereas liquid is better for drizzling over pancakes, waffles, etc and mixes easily with water or foods such as vegetable salads.
Finally, my favourite personal quote which sums up my sentiments regarding purity of honey:
"I believe the best labs can create synthetic liquids that look and taste like real honey and even have the same glucose-fructose molecular structure, but NEVER can they fake something that works the same as real honey for our health and well-being. Because the bees have added a MYSTERIOUS GOODNESS of their own that can never be comprehended by the most ingenious mind or counterfeited by the most advanced technology." ~ Ruth Tan