Paraffin
Paraffin is a petroleum byproduct, cheap to produce, and it holds and releases fragrance oil very efficiently. That last part is why it persists despite its reputation: paraffin generally throws scent harder than the alternatives at the same fragrance load.
It burns hotter and faster, which shortens burn time, and it is the wax most associated with visible soot when a wick is left untrimmed. The health claims made against it in marketing copy are considerably stronger than the published evidence supports, and the same is true of the health claims made for its competitors.
Soy
Soy is a vegetable wax that burns cooler and slower, so a soy candle typically outlasts a paraffin candle of the same weight. It holds less fragrance oil before it starts to misbehave, which is why soy candles often read as subtler.
Soy is also temperamental to pour. Frosting, wet spots against the glass, and uneven tops are cosmetic quirks of the wax rather than defects, though they are why some makers blend rather than pour pure soy.
Coconut and blends
Coconut wax burns slowly like soy but carries fragrance better, which is why it has become the default in the premium tier. It is expensive, and almost nothing sold as a coconut candle is pure coconut wax. Most are coconut-soy or coconut-apricot blends.
Because blend ratios are almost never disclosed, the word on the label tells you less than you would like. Judge a blend by burn time and throw rather than by its name.
What this means for what you buy
If you want the strongest scent in a large room for the least money, paraffin or a paraffin blend still wins on the arithmetic. If you want the longest burn and a softer scent, soy does that. Coconut blends sit in between and cost the most.
None of these differences justify a threefold price gap on their own. When a candle costs $70, you are paying mostly for the vessel, the fragrance formulation, and the brand, not for the wax.