The German mathematician and philosopher Gottlob Frege, in discussing his linguistic theory of sense and reference, showed how two different terms could have the same reference, but different senses. His famous example is "the morning star," and "the evening star." Both terms refer to the planet Venus. So, they have the same reference (denotation). But, they have different senses (connotation). (See here; scroll down to 3.2.)
The terms "Christian" and "follower of Jesus" used to have the same reference, with different connotations. Such is the case no longer.
At one time, "Christian" meant "follower of Jesus." "Follower of Jesus" was, perhaps, a subset of the broader category "Christian."
It was assumed, in the first century of Christendom, that if a person was a "Christian," then they followed the life and ways and teachings of Jesus. This is why Christians were martyred, like Jesus was. This is why Christians were peacemakers, and lovers of people, even their enemies. This is why Christians forgave one another, and why they served one another, since Christ came to serve, not to be served.
No longer is this the case.
Many self-refer as "Christian," but have little or no intention of actually following Jesus. I point out, e.g., that they must love other people, even their enemies, and that they must forgive others from the heart and not hold on to bitterness, and that they must not accept relationship division, since Jesus calls us to be reconcilers and peacemakers. Which means, to go after these things, behaviorally. Many, it appears to me, want the name, but not the cross.
Today, it is possible to think of oneself as a Christian, but not give Jesus the time of day. You can be a Christian and not follow Jesus. You can be a Christian but have no time to pray. You can be a Christian, while popping in and out of church. Your entire family can be a bunch of Christians, yet your hearts are won over by secular commitments.
Which means: "Christian," and "follower of Jesus," have neither the same sense, nor the same reference.
This is why we must abandon the word "Christian," and decide whether or not we will be disciples of Christ, people who hear Jesus' voice, and obey.