The Adirondacks, geologically speaking, are not part of the Appalachian mountain chain though they are often grouped with it because of their location. While the Catskills are part of the Appalachians, the Mohawk and Hudson river valleys separate them from the Adirondacks.
The other key difference between the Adirondacks and the Appalachians is that the Adirondacks were formed by an uplift, and the mountains in that range are still growing.