Agape means love. According to Matthew Henry, the KJV translators used the word charity to indicate when the context was referring to both love towards God AND towards man, whereas when they translated it specifically as love, only one of the two was in view.

It makes more sense to tell Peter to feed His sheep than to say be a shepherd to them. This focusses more on what he was to do with the believers, rather than his vocation (ie. spiritual shepherd).