Any difference in meaning between "Jesus Christ" and "Christ Jesus" is slight, because they mean essentially the same thing but with a slightly different emphasis depending on the order of the names. To understand the subtleties, we will look at what each name means on its own.
Do Jesus Christ and Christ Jesus mean the same thing?
When Mary gave birth to the Son of God, she and Joseph, her betrothed, were instructed to name Him Jesus (Luke 1:31–32; Mathew 1:21). Therefore, the name "Jesus" is the human name that was chosen by God to be given to the Son of God when He became incarnate. While Jesus is a personal name, Christ is a title that means "Messiah," "Anointed One," or "Chosen One." Having "Christ" next to "Jesus" ascribes honor to Him whether that title is placed first or second.
When reading the Bible, it seems these two names are basically interchangeable as far as the order they could or should be used. Some passages put the title first: "Grace, mercy, and peace from God the Father and Christ Jesus our Lord" (2 Timothy 1:2). Others put the human name "Jesus" first (Jude 1:1). So, what is the difference? The difference lies in which name comes first. Putting "Christ" first may emphasize the divinity of Jesus, while putting "Jesus" first may be a more personal way of emphasizing His humanity.
The apostle Paul, in Philippians 2:5–11, shares a writing that was probably an early Christian hymn passed through oral tradition to help believers maintain their Christian theology. This passage begins by talking of how Jesus was emptied and became a servant by taking on flesh, coming in human form. It ends by talking about His final ascent into heaven. The beginning of the hymn refers to Him as "Christ Jesus" and the end of the hymn refers to Him as "Jesus Christ." It would seem that, in this particular passage, the order of the names could represent the direction that Jesus is going: "Christ Jesus" (heavenly title to human name) refers to the God who became a man, while "Jesus Christ" (human name to heavenly title) refers to the man who was truly God and ascended to His rightful place in heaven.
Putting "Christ" first could also be the more formal of the two options. For example, some have observed that Paul, who did not physically walk with Jesus, uses "Christ Jesus" more frequently than the other apostles. John, who physically walked with Jesus, only ever refers to Him as "Jesus Christ."
To sum it up, any difference there may be between "Jesus Christ" and "Christ Jesus" is subtle in nature, and most likely insignificant. Putting "Christ" first places a small emphasis on the deity aspect, while putting "Jesus" first places a small emphasis on the humanity of our Lord. No matter how your order it, Jesus is Christ the Messiah, the Son of God.
What does 'Christ' mean?
What are the names of Jesus Christ? What titles are ascribed to Jesus in the Bible?
Who is Jesus Christ?
What is the significance of the humanity of Jesus?
What is faith in Jesus? What does it mean to have faith in Jesus?
Truth about Jesus Christ