Faith healers are funny people. They are generally selective about who they heal, and when they've selected their marks, they may even invent false symptoms, which they will then "cure". They'll make use of the placebo effect, they'll pressure people into just going along with them, they'll even use a number of clever tricks to make it look like they're doing good.
But not Jesus. Jesus wasn't selective about who He healed. Those who asked for healing, no matter how seriously they were injured, no matter how severely sick they were, one touch and Jesus healed them. Lepers, the deaf, the lame, the blind, even if someone was actually dead, Jesus didn't even need to touch someone, they were healed by nothing more than the fact that He had healed them.
False teachers are funny people. Much like faith healers, they claim to have great spiritual cures for great spiritual ills. They have a number of clever tricks to make their religion, or their denomination, or even just one false doctrine seem great. But just like faith healers, they're powerless. Their doctrines cure nothing. Their paths lead to only one place: Hell.
But not Jesus. Jesus' miracles, great though they were, were not just some party tricks, or some great humanitarian aid. They were the divine equivalent of showing His ID badge. These were Jesus saying "just as I have the power to heal you physically, I have the power to heal you spiritually." There is no sin you can commit that He cannot free you from, and forgive you for, and the great thing about that is He's not entirely selective about it. All who come to Him in faith will be saved.