Excellent question, and the answer depends partly on how we define the words. The Greek word for “disciple” literally means a learner. It could in its broadest sense refer not only to Christians but also to “God-fearers” like Cornelius in Acts 10. The term “Christian” means a “Christ-follower.” In the New Testament it means one who has made a personal commitment to Christ. Given that understanding, the following statements are true:

All Christians are disciples, but not all disciples are Christians.
All Christian learn from Christ, but not all who learn from him end up following him.