Is 'honey in crystallized form' the same as 'raw honey'?
Subquestion: can heated/pasteurized/decrystallized honey ever crystallize again?
Short answer? Maybe. Crystallized honey and raw honey are not mutually exclusive, so you may have a honey that is one or the other, or you may have a honey that is both.
Raw honey is simply honey that has not been over-heated (heated more than necessary to allow the honey to flow for easier bottling) or pasteurized.
All honey will eventually crystallize; however, raw honey will crystallize faster than pasteurized or heat-treated honey, which is often of lower quality as the heat required for pasteurization destroys some characteristics of the honey.