Same last name. But whether they are named for the same person I don't know. Butler was a revolutionary war soldier who settled at the confluence of the Kentucky and Ohio Rivers. From the family estate, there were several generations of high ranking soldiers through the Civil War, Mexican-American and more.
Here's a little info from the park website: Named for General William Orlando Butler, the familys military fame spanned from Colonial times through the American Revolution, the War of 1812, the Mexican War and the Civil War. Obviously Butler is a common last name with Butler Counties in several states. But with Orlando as a starting point, you should be able to google or wiki if you want to research the rest of the history.
One unique feature of this park (at least for Kentucky) is several abandoned ski slopes with the rusty remains of light poles, snow making equipment, and warming shacks. After the harsh, snowy winters in 1977-78, several ski resorts sprang up in southern Ohio and Indiana, with Kentucky State Parks getting into the act at General Butler. For many years following, winters were mild, and warm, with more rain than snow. After several unprofitable years, most of the resorts closed; Perfect North Slopes in southeastern Indiana being the notable exception.
I didn't know the park was in KY...
BUTLER COUNTY was formed in 1803 from Hamilton and named from General Richard BUTLER, a distinguished officer of the Revolution, who fell in St. Clair’s defeat. from ancestry.com
Hamilton must have been quite a large area and not just a town back then.