especial, especially, special, specially
1. There is no longer any great difficulty with especial because special has all but driven it out, although it is still used occasionally to refer principally to exceptional personal qualities or attributes as in your especial charm. The adverbs specially and especially present a much bigger problem, because each continues to the usurp the role of the other quite extensively. Essentially, the difference is this: especially means ‘chiefly, much more than in other cases’ and can qualify adjectives and adverbs as well as verbs, whereas specially means ‘for a special or specific purpose’ and qualifies verbs, participial adjectives formed from verbs (as in specially made), and occasionally (when it encroaches on especially, as described at 3 below) adjectives.
2. The following examples show this distinction: (especially)

• The sumo wrestlers are not especially tall, but they are especially big —C. James, 1978

• Ancient woods…are especially important for wildlife —Times, 1982

• Insist on listening to some music, preferably piano music that shows up wow and flutter especially well —Listener, 1982

• The transfer of Britain's most sophisticated technologies (especially in laser and micro-computing)…will have appalling effects on the British economy —City Limits, 1986

• (specially) This fine piano was made specially for us —Chicago Tribune, 1977

• I gathered these specially in bud, because I thought it would be nice to see them open out in the warmth of the house —D. Madden, 1988

• If it's suitable for your job, try using a plaster repair product as it's specially formulated to be easier to apply and smooth out than conventional plaster —Evening Gazette, 2007.

3. The meanings of the two words come closest when qualifying an immediately following adjective, as in the following examples in which each word is virtually interchangeable for the other, although especially is still the more correct:

• It's a pretty anonymous mark. Not one I'm specially proud of, either —Penelope Lively, 1991

• The function of the criminal law, as we see it, is…to provide sufficient safeguards against exploitation or corruption of others, particularly those who are specially vulnerable because they are young, weak in body or mind or inexperienced —T. Newburn, 1992.

Specially more usually encroaches on especially, but sometimes especially is the offender:

• ☒ The fiddler plunged his hot face into a pot of porter, especially provided for that purpose —Dickens, 1843

• ☒ These Pakistani garments are created especially for the wearer by a joint effort of the women of the family —A. Wilson, 1988.

Modern English usage. 2014.