"Especially" is used when you want to single out one or more elements as particularly important within a group or category.
"I love reading soft sci-fi, especially books by Isaac Asimov."
"The movie was great, especially the ending."
synonyms - particularly, above all, most of all.
"Specially" is used when something is done for a particular purpose, often custom-made for that reason.
"This lesson plan was specially designed for online teaching."
"I baked a cake specially for my mother's birthday."
synonyms - specifically, uniquely.
Just to recap:
- Especially is about emphasis and exceptionality among a larger context.
- Specially focuses on specific intent, purpose, or customisation.
