The PS2 emulator used on non-BC consoles is ps2_netemu, which was designed specifically to play PS2 Classics titles from the PS3 store. It uses its own disc format rather than ISO, and is encrypted because Sony didn't want you to use those games outside the PS3. On HEN the only way to play PS2 titles is to convert them from an ISO to the emulator's native encrypted format and play it that way. On CFW, there's a wrapper in Cobra that can inject raw ISOs into the emulator. It does not support physical discs though (neither original nor burned). Whether it's theoretically possible to modify it so it does support them, you'd have to ask Evilnat.
The only emulators capable of accessing real discs are the old ps2_emu and ps2_gxemu, which require hardware compatibility (the first is used on CECHA / CECHB and the second on CECHC / CECHE).
Regarding PS1, it has two emulators, ps1_emu and ps1_netemu, and unlike the PS2, they are both software based. The former is used for physical discs and the latter for PSOne Classics purchased from the PS3 store. Since they're both software based, all PS3 models support PS1 discs. Discs, whether original or burned, will always be played using the regular ps1_emu and by default so will ISOs, although you can force ps1_netemu to be used, which can solve some issues with certain games.