It depends a bit on the time frame of the reference. In centuries past, in the United States, they probably meant virtually the same thing - people with little or no possessions, opportunities or education who worked for landowners and were rewarded with some small share of what they produced. Today, many sharecroppers are established businessmen who contract with landowners to rent farm land, with their rent being a combination of a base fixed rent and a percentage of the revenues from the crops harvested. I personally know of one case (and I doubt it is the only one) where the sharecropper owned the land he now farms. A few years ago, with no descendants interested in taking over the farm, he sold the land, but kept all of his farm equipment and now rents the land from the new owner.

A sharecropper, as I understand the word (share+crop), farms on land owned by someone else and pays rent in the form of a portion of the land's harvest. The sharecropper does not own the land. The word peasant has several meanings, but in this context it is possible a peasant owns the land (a rich peasant).