We started with allowance to be for doing chores, but it quickly advanced to "how much will you pay me" if we asked her to do extra chores (for example, company was coming). So we changed it to allowance is the "sharing" of the money coming in from daddy and mommy working. We all get our spending money for the week at the same time (me and hubby included) so she knows we all get money to spend.
If she doesn't want to do her chores, we tell her that she can't "share" in the family money because she isn't helping the family. We don't pay per chore and we let her know she is expected to help. We leave what she is expected to do "open" so that she has her basic chores but also we can add things on if we need help. She's older, so she understands we are a "family" and we help each other. Just changing that viewpoint has helped get rid the "how much will you pay me?" attitude. Instead of us being the boss and her being the worker and us holding the money over her to do her chores, we approach it as we all work together. I hope that makes sense!
I wouldn't make your 4-year old put money away just yet. At age 6 my daughter didn't understand that and it just led to disappointment that she couldn't keep her whole allowance. Once we finish studying money and banks, we'll start making her save. Until then she just thinks we're being mean.
Just my opinions, hope that helps!