Most things with CD tried to be backwards compatibility, most things with cartridges not so much.
That's not really accurate. Sure the Playstation line was Backwards compatible up until half way through the PS3's life span but none of the Sega Disc based consoles were BC. However Sega's Genesis could play Master system games with the appropriate adapter. (the adapter was really only there for the slot to accept the cartridges). Also the Atari 5200 and 7800 could play 2600 games. The gameboy's were almost all backwards compatible through that entire lineage and now the DSs are are almost all backward compatible through their lineage. And those are all cart based. The Wii could play GC games but the WiiU could play Wii games but NOT GC games. All of Microsoft's consoles were only semi-backwards compatible since it's really just emulation and support was added on a game by game basis. Then you have other weird stuff like the Super Nintendo could play Game Boy games and the GameCube could play GameBoy Advanced games.
My point being that there's no general rule when it comes to this stuff, the compatibility from generation to generation is inconsistent since support just comes down to a cost-benefit analysis for whoever made the console.