A Pillar of Strength, or Column of Apathy?

Is there a difference between being emotionally strong, and simply not caring as much as the next person?

A person is a source of emotional strength is able to deal with other people's problems without letting it affect them too much. They are able to listen and aid without becoming drawn down into the muck themselves.

If a person simply wasn's invested in your emotional well being, could they not do the same thing, with less authenticity or with less care for the outcome of their advice?