With the candle you have a solid well below flash point temperature. The wick when lit becomes a source of heat melting a small amount of the wax. The wick further absorbs the melted wax where it is heated to the flash point, hence the flame continually feeds itself until all of the wax is consumed or more often the wick is consumed leaving a glob of wax that was melted ran off and not absorbed by the wick.
Like was said wax is flammable, inflammable, combustible, ie it will burn. What it is not is explosive, though hot wax like gasoline when it flashes certainly does look explosive. BTW, gasoline is not an explosive either.