Chiefs is a term to denote a leader or leaders or head figure. More specifically for the team version it denotes the leaders of an Indian tribe. Much like the term "General", "President", etc
Redskins is a derogatory term that people used in a negative tone towards Indians for centuries. Much like the terms "Cracker", "The n word", etc.
Kind of a difference. But you're right I'm sure some puss will complain about it at some point. Some have tried to get Cleveland to change their team from the Indians before. Redskins is the only term that people actually have any footing to stand on when complaining though... or at least so far.
Edit- as far as the tomahawk chop goes... Not sure how that's offensive. I guess it could be offensive to the oppressed white people with ancestors who were once scalped by Indians. And yes that was meant to be sarcastic.