Hi,
I'm not going to repeat all the definitions you will find in a good dictionary. Instead, here are some brief general comments on common meanings and usage levels.
"academic" Quite a common word. Related to learning. Often used for people or activities in an institute of higher education, eg a university.
"scholastic." A less common word (although used in speaking of 'scholastic' supplies, eg pens, paper, etc. for students in schools). Can be similar to 'academic', but may also be used for people and activities outside a formal university-type setting. A 'scholar' can be either be a person at a university or someone who pursues knowledge diligently on his own, eg at home.
"differences" Commonly used. The way in which things are not alike. eg I think there is no difference between Coke and Pepsi.
"differentiations." Less often used. When it is used, it is usually in the form of the verb 'to differentiate', with the meaning of 'to find differences'. eg I can't differentiate between Coke and Pepsi.
Best wishes, Clive