The Irish are particularly sensitive to this difference. It is believed that St. Patrick, an actual man who was a Christian missionary in Ireland, used the shamrock to explain the holy trinity, which apparently went really well.
In contrast, the four-leafed clover is a rare genetic mutation of the three-leafed variety. While associated with luck, they are not considered to be shamrocks by those passionate about Irish tradition.
Now you have something cool to share with your drinking buddies. Happy St. Patrick's Day!