The fact is, every true Christian IS a disciple of Jesus. The word disciple is used consistently to describe believers in the book of Acts, and any distinction between the two words is purely artificial.
However, the problem is this: Modern Christianity has separated the two terms, which has given birth to easy-believism that ignores (or disposes of) the hard demands of Jesus. Ergo, not everyone who calls themselves a believer is a believer. They merely profess Christ while their life bears no evidience of salvation. This lack of fruit is then explained as being “only saved” but not yet a disciple. This is false because Jesus clearly stated that one of the evidences of being a follower/believer/disciple (whatever term you want to use) was being fruitful (John 15:8).
When Jesus called followers, He always instructed them about the cost of following Him right up front. His invitation to salvation was never easy-believism. Halfhearted people who were not willing to make the commitment did not respond. Thus He turned away anyone who was reluctant to pay the price or meet His terms. Therefore, they were not Christians because they were not willing to be His disciples.