These words are widely used interchangeably, with special being more common. There is a distinction in meaning, however. Especial means "exceptional," "outstanding," and special means "of a distinct kind," "particular," "individual": "This rule is of especial importance to all members of the club." "Jack is a special friend of mine." The adverb especially is more widely used than specially, perhaps because it embraces the meanings of "chiefly," "principally," "notably," and "mainly": "Last year we had an especially severe winter."
Dictionary of problem words and expressions. Harry Shaw. 1975.