What's the difference between specially and especially?

http://www.learnersdictionary.com/qa/what-s-the-difference-between-specially-and-especially

The following is derived from the above site.

What is the difference between specially and especially? – Mary, United States

The meanings and usage of these two similar-sounding words overlap quite a bit, so it can be hard to figure out which one to use when. If you are interested in the details, I encourage you to read their entries in Merriam-Webster's Learner’s Dictionary. If that’s more information than you need, here are simple rules to follow that will insure that you are using these words correctly:

1. Use especially to mean “very” or “extremely,” as in these examples:

There is nothing especially radical about that idea.
The food was not especially good.
She loves flowers, especially roses.

2. Use especially when something stands out from all the others, and you want the meaning of “particularly,” as in these examples:

She can't be sure she will win, especially at this early stage of the campaign.
The appetizers and especially the soup were delicious.

3. When you want to convey the meaning “for a special purpose,” or “specifically,” you can use either especially or specially. They are both correct.

The speech was written especially/specially for the occasion.

4. When you want to convey the meaning “in a special manner”, as in this example below, use specially. In this context, especially would sound odd or wrong to most native speakers.

I don't want to be treated specially.
I don't want to be treated especially.

especially

ADVERB

used when mentioning conditions that make something more relevant, important, or true

specially

ADVERB

in a particular way, or for a particular purpose

uniquely

ADVERB

especially

particularly

ADVERB

used for emphasizing that something refers especially to one specific person, thing, or situation

notably

ADVERB

FORMAL especially: used for introducing a good example of something

in particular

PHRASE

especially

ADVERB

used for showing that what you are saying applies to one person or thing more than others

especially

ADVERB

for a particular purpose or for a particular person

esp.

ABBREVIATION

especially

above all

PHRASE

used for referring to something that is more important than any of the other things you could mention