In fact, the difference between the two is partially illustrated by Abraham's treatment of Hagar and Sarah. Recall:
Galatians 4:30-31The difference between bondwoman (Hagar) and freewoman (Sarah) could hardly be more stark.
Nevertheless what saith the scripture? Cast out the bondwoman and her son: for the son of the bondwoman shall not be heir with the son of the freewoman. So then, brethren, we are not children of the bondwoman, but of the free.
Our wives (in Western societies) are not slaves. We don't even have wives who are also slaves as did some of the Israelites. The may grumble about their domestic duties being some form of slavery, but truly they are not slaves or equivalent to slaves.
What about our children? They may also grumble about being "slaves," but there is more merit to that particular grumble. Recall that Scripture says (in close proximity to the discussion above):
Galatians 4:1-2Of course, there are some important differences between slaves and children. Nevertheless, there is a comparison that can be legitimately made there.
Now I say, That the heir, as long as he is a child, differeth nothing from a servant, though he be lord of all; but is under tutors and governors until the time appointed of the father.
I don't say that to encourage you to permit your children to grumble that you treat them like slaves. Rather, when they do, here's your chance to redirect the conversation to Scripture.