cure : 主要指治愈疾病。
At one time doctors couldn't cure TB/cure people of TB.
医生曾经无法治愈肺结核/肺结核病人。
heal : 侧重指治愈伤口、伤痛如灼伤等。
The wounds were gradually healing (up).
伤口在逐渐愈合。
The plaster cast helps to heal the broken bone.
石膏绷带有利于断骨的愈合。