You’ve received several responses but the meaningful “come to Jesus” story actually relates to Saul (Paul, who is responsible for much of Christianity) on the road to Damascus.

Paul was persecuting primitive Christians and while he was traveling to Damascus to arrest them, he was temporarily blinded by divine intervention that led to his conversion and stopped him from continuing to persecute people. The dramatic intervention disabused him of the errant beliefs that caused him to injure people, in other words.

See: https://en.m.wikipedia.org/wiki/Conversion_of_Paul_the_Apostle

That’s what the comparison is talking about. It’s a metaphor that relates to needing a dramatic and often violent wakeup call to snap someone out of doing something wrong. From a Christian perspective you can see how Paul being shaken up enough to change his name, religion, profession, etc was a real “come to Jesus” moment.

That’s the key context I think you’re asking about. It’s not really about converting to Christianity. It’s more about having a BIG wakeup call that you’re on the wrong path (literally in Paul’s case) and you need to change your ways because you’re hurting people (or you’ll stay blinded if you’re Paul I guess).

Hope that helps!