jb bore paste vs 40-x

Once used 40-x say 7 years ago, it worked well on copper, not at all on lead.  It used to be a greasy runny grey liqoud that had a ball bearing in the bottle that would mix it up when shaken. 

CURRENT version is a slightly runny clear liqoud, that actually works on copper residue in a hand gun. 

JB bore paste is a thick grey/black slime that works super good on lead and not at all on copper in a handgun barrel. 

My question is, are these two products related to each other in anyway

The item with the ball bearing to mix it up was Rem-Clean. It has a similar abrasive to JB Bore Paste but as you say, it is oily.
Both products are primarily meant to break down carbon, and to some degree will remove some lead or copper fouling.