There are CECHA & CECHB they are fully backwards compatible because they literally have PS2 hardware inside of them. Well folks lost their marbles seeing the $600USD price tag.
Sony in their infinite wisdom to cut cost made the CECHC & CECHE models with half the hardware taken out, the emotion engine thus relied on some emulation. Compatibility went from 98% to around 75-80% for PS2 games. These were the only models capable of playing PS2 disc.
Refered to a BC & semi-BC PS3's. But note only Japan and North America got the full BC units. And everything else as non-BC as it can not play disc only PSN style games which you had to buy all over.
So they were no longer backwards compatible but Sony had a new avenue to charge for emulated games till an exploit was found. There is only a handful of official games but now we have folks making config files to add more to the available library. And bringing the list percent up but still below 50%