No distinction between the words healing and curing

I suppose I never really thought much of this until an Arminian said it. But an Arminian once said that healing people and curing people are two different things. He bolstered his claim by using the text of scripture to suggest that Jesus healed people from demonic possession but didn't really cure them of it. Just think of what this satanic man is saying... Jesus doesn't save unto the uttermost. However, etymologically speaking the word for healing is synonymous with the word curing. The text he uses doesn't really prove his point either. What is also sad is that this guy is a teacher at a school. He has a degree somewhere. He ought to know what words mean. The hokie pokie was his favourite song.