treat : 对某人，疾病，伤害等给予医疗或护理（通常为被动形式） —— 强调“护理”
She was treated for sunstroke. 她因中暑而接受治疗。
The condition is usually treated with drugs and a strict diet. 这种病通常用药物和严格控制饮食进行治疗。
cure: 使人或动物生病后再次健康 —— 强调“治愈/康复”
TB is a serious illness, but it can be cured. 肺结核虽然是一种严重的疾病，但可治愈。
Will you be able to cure him, Doctor? 医生，你能把他治好吗？
heal: ——侧重指治愈伤口、伤痛如灼伤等。
It took a long time for the wounds to heal. 伤口过了很长时间才愈合。
The cut healed up without leaving a scar. 伤口愈合没留下疤痕。