Shelly is just a loose term for green shelled beans. They are harvested before the pod dries, but after it has filled out and started color change. Some cultivars used as shellys can be harvested young as snap beans. These are dual purpose. Both terms refer to usage.

Some shelly beans have pods that remain edible even when they start to change color. I sometimes steam them pod and all at that stage. Striped Cornfield and Goose/Ma Williams are examples.

Some beans such as Tennessee Cutshort and Tobacco Worm have seeds that are smaller than most of the shellies but they are still best eaten after the pods swell as sort of a combination snap and shelly bean.