In general terms within Disney Infinity, an Ability is a character's "power or capacity to do or act", regardless of their knowledge. This includes a number of Basic Abilities that are unlocked by default, as well as Special Abilities that, while not as common, are areas that further define the character.
In general terms within Disney Infinity, a Skill is a character's power or capacity "to do something well". For example, while any character may pick up the lightsaber toy and swing it about, only a Lightsaber Master can develop the skill to its full potential. Additionally, while many Abilities are unlocked by default, most Skills must be unlocked by spending Skill Points in a character's Skill Tree.