One of my bosses is also a family friend of several years that my family shares most everything with, so this boss is aware (and is supportive of the fact) that I'm currently looking for something full time in my field, but am still committed to the work I have now.

My other boss has no idea and there really isn't a need to communicate that. I get along great with this boss, but my relationship with them only extends to work. They weren't invested in me as a person before I was an employee. That, in my opinion, is the only exception. Otherwise else, no need to say anything until another position is guaranteed and you need to provide notice in preparing for your leave.