I think they are both B&C stocks. The Kevlar stock was designed to be use with the Ultra Lite. I have been told that Knight will sell the Kevlar stock separately as of late. While early they would not. The only way to find out is email or call them and inquire.
If Knight sent you a composite stock from their stock it should fit and/or require very little work to get it to fit properly. You should not have to press fit the rifle in the stock.
Your pictures... the stock is designed to accept both style of recoil lugs. The square lug like you have or the Forked Recoil lug. Most feel that the Forked lug offered better stability in the stock.
So let me ask this.... When you set your Super DISC in the new stock, where is getting the stuck feeling? Under the receiver or in the barrel channel. When you go to install the rifle in the stock you should be able to physically press the receiver in. You should not need to use the recoil screw to pull it down to a seat. Actually, it should just set in the stock. It is not uncommon but not normal that the barrel does not just set into the barrel channel. In fact if the barrel is sticky going into the stock - you will more than likely have accuracy problems.