I guess my kids have a few assigned chores, but mostly they just help out as needed. The things that are almost always their jobs are setting the table (they take turns), the yardwork (ds 15 likes to do that), the garbage and the vacuuming (ds 13 does those because he doesn't like yard work.) They also keep their own rooms clean and put away their own laundry, but that's sort of a given.
Things they often help with are dinner preparation and cleaning up, keeping the laundry going, etc. Because I only work part time I still do most of the basics like cleaning the bathroom, mopping, etc. but they know how and can pitch in if I'm not feeling well or get too behind.
It seems unusual to me that a two year old would have "chores," but it's apparently just semantics. My kids have always been taught to clean up after themselves since their earliest memories. If putting away toys is a chore, they had chores from the time they could walk! We also had a mini broom, a mini mop, etc. and they often just worked with us as part of their daily play.