there are 2-4 ps2 emulators ps2soft_emu and ps2net_emu (and ps2gxemu and ps2emu)
heres a good explanation about the difference between them
*PS1_Emu.self - Introduced in the Firmware 1.02, this is the earliest build of the PlayStation Emulation,for the PlayStation3, still used in the current Firmwares, this Emulator has the ability to load Optical Disc media, and has a compatibility rate of 98.7%, it runs entirely on Software, being Emulated through the CELL B/E and RSX, it doesnt rely on any of the PlayStation2 Hardware to achieve Backwards Compatibility, Configurations are hardcoded through the Emulator executable Self File.
*PS1_NetEmu.self - Introduced in the Firmware 1.70, this version has no Optical Disc Support, it was introduced as part of the PSN PlayStation One Classics program, to excecute Titles purchased from PlayStation Network, the save data wasn´t written in a Virtual Memory Card,but rather on a proprietary format, that could be shared between the PlayStation Portable and PlayStation3, in Firmware 1.80 the PS1_Emu/Net_Emu was granted the ability to Upscale PlayStation and PlayStation2 Software Format, Compatibility was also improved.
*PS1_NewEmu.self - Added in Firmware 2.10, its a improved version of the PS1_Emu.self, but granted the ability to play PlayStation One Software Format through Remote Play, with the PlayStation Portable of an Optical Disc Media, PlayStation Compatibility was
improved.
PlayStation2:
PS2_Emu.self - Introduced in the Firmware 1.00/1.02, this is the earliest build of the PlayStation2 Emulation of the PlayStation3, this Emulator Self, required 99% of the PlayStation2 Hardware, this being the Emotion Engine + Graphics Synthesizer + EDO RAM, to achieve PlayStation2 Backwards Compatibility, the Emulator has support for PlayStation2 Optical Software Format, it was compatible with 98% of the PlayStation2 Library, this self Emulator was only compatible on the Fully Backwards Compatible Models - CECHA/B PlayStation3 Models, PlayStation2 peripheral was also supported such as the SCE/Broadband Network Adaptor, beyond 98% of the peripheral for the PlayStation2 was supported on the PlayStation3, DualShock2 Pressure Pads Function was also Compatible with the DualShock3 in PlayStation2 Backwards Compatibility,and PlayStation Portable as well for the selected titles.
PS2_GxEmu.self - Introduced in the Firmware 1.50, this is a modified version of the PS2_Emu for the newest PlayStation3 Board Revision, COK-002, the Emotion Engine + EDO RAM were removed, and the EE+EDO Tasks were moved to the CELL B/E and the XDR RAM, only the PlayStation2 Graphics Synthesizer remained, the Emulator Self has support for Optical Disc Media like the PS2_Emu,as well support for any PlayStation2 peripherals, and DualShock2 Pressure Pads Function was also Compatible with the DualShock3 in PlayStation2 Backwards Compatibility, PlayStation Portable as well for the selected titles, since the EE and EDO RAM were Emulated, Compatibility decreased from 98% to approximately 94%, titles that required the original Emotion Engine functions either were incompatible or the title didnt preformed as intended, this Emulator Self, its only Compatible with the PlayStation3 Models - CECHC (PAL) and CECHE (NTSC), these are dubbed as Partial Backwards Compatible.
PS2_SoftEmu.self - Introduced in the Firmware 1.90 with the release of the CECHG Model in 2007, this Experimental Emulator was another modified version of the PS2Gx_Emu.self, in an attempt to retain PlayStation2 Backwards Compatibility on Non-PlayStation2 Hardware, relying only on Software Solutions, $ony removed the PlayStation2 Graphics Synthesizer, from the new Board Revision "SEM-001" and moved the GS task to the Reality Synthesizer GPU, unfortunately Emulating the Graphics Synthesizer was deemed inefficient, as the Nvidia/RSX GPU wasn´t capable enough to Emulate the Graphics Synthesizer on his own, so the Emulator was only for Internal Testing purposes, as performance was very poor, Compatibility was around 10% maybe a bit more, the Emulator had support of PlayStation2 Optical Disc Support, peripheral its unknown, the Emulator could be acessed in Factory Service Mode, until Firmware 4.21, later it was removed completely.
PS2_NetEmu.self - Introduced in the Firmware 3.70, as part of the PlayStation Classics Program for the PlayStation Network, this Emulator wasnt mean´t to be a replacement for PS2_SoftEmu,but rather a brand new PlayStation2 Emulation Solution, compatible with Select PlayStation2 Titles, this Emulator has no Optical Media Support,as it wasnt designed to work with any of the PlayStation2 Disc Media Format,but rather Encrypted ISO/BIN Formats provided by $ony Computer Entertainment Platform Holder, and they´re respective Publishers, the Emulator doesnt have any PlayStation2 peripheral support, nor DualShock2 Pressure Pads Function, peripheral support were mostly PlayStation3 Only, with the exception of the GunCon, the PS2_NetEmu on Custom Firmware Mode, has a Compatibility rate of 65/70%, it can be increased with External Configurations File, the same Configurations are present on Original PlayStation2 Classics Titles found on the PlayStation Network in PKG Format, in the Emulator is executed in PSN Format, the Save Files cannot be interchangable,as it has a proprietary format on the PS2 Save Data Colum, when executed in Cobra Payload Mode (Custom Firmware), the Emulator can save normal PlayStation2 Virtual Memory Card format, being compatible with the PS2_Emu/GX_Emu and SoftEmu, the Emulator is compatible across all PlayStation3 Models.