There's a definitional difference between the two words. "To accept Christ" suggests that I'm passing judgment on the Lord Of The Universe: to accept or not to accept (holding my chin in my hand, weighing the pros and cons of allowing Him into my life)? "To believe in Christ" is to trust Him to save, based on His redemptive work on the cross.
Yes?
Carlyle's acid rejoinder was, "By Gad - she'd better!"
I've always seen it as accepting Christ's grace and His lordship in your life.
Belief merely indicates that He exists. Even Satan believes in Christ. Satan knows all about Christ, yet is eternally damned.
"Accepting Christ" does not imply passing judgement on God. It's more like accepting a gift from someone--you're not passing judgement on them.