Special means that something has an identity, quality, purpose, or character all of its own, therefore it cannot be compared to anything else.
Especial means distinctive, noteworthy or of certain importance in comparison with something else, thereby implying that something of lesser value exists.
They are both used to mean out of the ordinary or exceptional.
If you need an adverb with –ly at the end of it, you will usually use especially, as it means particularly or exceptionally. However, if you want to stress the distinctive purpose of something custom-built, use specially.
He enjoyed the desserts, especially the chocolate cake.
The chocolate cake was specially made for him.
Profound Quote of the Day:
“I am neither especially clever nor especially gifted. I am only very, very curious.”
– Albert Einstein