"Indifference", as has been agreed upon, arises out of lack of care or concern.
"Equanimity", on the other hand means an equal care and concern for every other being.When we have equanimity, we treasure every being as equally precious. There is no separation of "I" and "others" .We recognize that each and every being equally desires happiness and does not wanting suffering.With equanimity, there is no more labeling and categorizing of people(for instance) as 'friends', 'enemies ' and 'stranger'. Labelling become meaningless, when in cyclic existence, enemies and even strangers, have been our friends in a previous life.When we have equanimity, we will not have hatred, attachment or indifference. Yes, equanimity arises from 'wisdom' ,and leads to peace
We develop equanimity, when we realize that all beings have been our mothers before. In 'Liberation in the Palm of Your Hand'(p.524), it is established, by logic, that "since we have had more rebirths than there are sentient beings, not only must they have been your mother, but also every single one must have been your mother in human rebirths. Thus it is reasonable to conclude that all beings have truly been your mother".