Matter and care have the same meaning but they're both used under different terms such as: Care－＞caring about someone "I care about you" Matter is is used when you are talking about a certain situation, something. "Our friendship matters to me" Matter can also means: question, subject, problem, case.

Your English isn't bad at all. You'll be surprised at the number of people who can't even form the questions starting from "what's the difference between..." properly. Myself included.