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Both were able to heal people using extraordinary measures.
Clark/Superman helped/rescued people but I can't think of a single instance where he actually healed someone. smile **

As for a glimpse into the origins of Superman and how Jerry Siegel envisioned the character... Superman - Man of Tomorrow

**ETA: Yes, he turned back time in the original Superman movie to undo Lois' death, but that wasn't a healing, it was turning back time.

Lois: You know, I have a funny feeling that you didn't tell me your biggest secret.

Clark: Well, just to put your little mind at ease, Lois, you're right.
Ides of Metropolis