J-11A is Su-27 kit provided by Russia and assembled in China with Russian avionics. IIRC the original negotiation was for 200 Su-27 to be assembled in China with Russian provided kit (the so-called J-11A). However, PLAAF was not satisfied with the performance of J-11A (mainly the Russian avionics), so Shenyang developed J-11B, which is something like J-11A but with Chinese avionics.
The production of J-11A was cut short to ~100 units, and after that, they switch to producing J-11B. Reportedly the Russians were unhappy at that result (Cause using RU avionics = spare part dependencies = more Forex for Russia) and it caused all those rumors/reports about tension in further flanker procurement.
I'm not sure if the structural parts of J-11B are made in China or still using RU supplied kit, but it definitely uses Chinese avionics. J-11BG itself should be the MLU upgrade of J-11B. Not sure if there are any new build ones or PLAAF just buy more J-16.