Yes, there is a possibility of having different hair and beard color naturally. Each hair follicle contains coloring pigment. These coloring pigments are named as pheomelanin (which causes reddish and yellowish color) and eumelanin (causes blackish to brownish shades). It depends on the amount of these pigments in hair follicles. If hair follicles have dominant eumelanin, head hair will be of black or brownish shade. If beard follicles have dominant pheomelanin, your beard will be of reddish to yellowish shade depending on the dominance.