The main differences are feedstock, burn quality, and whether it’s “charged” before use. Good biochar is made from clean untreated wood/plant material, burned hot enough to carbonize well but not turn to ash, then crushed and pre-loaded with compost/urine/nutrients/microbes before going into soil. “Natural lump charcoal” is often very similar to biochar if it has no additives, but raw charcoal can temporarily tie up nutrients unless you charge it first.