I think it all comes down to how the words are typically used in everyday speech. Labor is typically associated with economic gain (or general economic activity) (or pregnancy) while chores generally aren't. I know I often hear people use the word chore when talking about errands or tasks they must perform for which they won't be compensated directly by another party (like taking out the trash as a chore).

I think we started off on the wrong foot with the comparison. Even government recognizes some difference between chores and labor, as childhood labor is illegal but it's not illegal to have your kids mow the law (afaik).