Christian punk is basically punk except that it is for christians. They listen to punk music, but generally go for the music that doesn't swear a lot. It's a more tame version of punk, except they hate "improper authority" (authority that they believe shouldn't be in the authoritative position of power) as much as general punk hates "all" authority. They wear clothes identical to both neo-punk and just general punk.
You see that kid over there who looks like a skater with the cool hair? Yeah, he's Christian Punk.