Paul testifies before Felix, one of the Roman authorities, and is also confronted by some of the Jewish authorities. The Jewish leaders claim that Paul is a "ringleader of the sect of the Nazarenes" (Acts 24:6). Jesus, being from Nazareth, is identified as the leader of a sect. But Paul won't have any of that, claiming, "that according to the Way, which they call a sect, I worship the God of our ancestors" (24:14).
So what's the big deal? Who cares is his detractors call him a Nazarene and he says he belongs to the Way? Isn't that just like the difference between being an Episcopalian and a Methodist?
Well, no, actually. Because it is a definitive statement on who Jesus is.
If Paul claims that he is a Nazarene, that means that Jesus was primarily some guy from Nazareth. He lived, had some followers, but then died. All in all, the most important part of Jesus was that he was from Nazareth.
But this isn't the case, and that's what Paul is contending when he claims that he worships God according to the Way. For Paul, Jesus was much more than some man from some forgotten little town. Jesus is living, having been resurrected from the dead. Paul follows the Way of Jesus, he doesn't just acknowledge that he's from Nazareth.
For us, it's the difference between saying "I believe in God" and "I follow God." We can believe all sorts of things but never do anything about it. I believe that the world is round, but that doesn't change my life. But I follow Jesus, and that one fact has changed my entire life. And indeed, it has changed the life of the world.