Orchid doesn't disable passives, Doom isn't just a silence, it's much more bigger than it. And enemy can't use items. And existing items stop working (like battlefury, or orb effects (even lifesteal!)). Even this pesky Slark will be visible and won't regenerate under his ult, so basically, his "hit and run" tactic won't work. Or you tired of enemy Huskar being invincible due to his magic damage reduction? Well you know the solution! (Doom). Or maybe enemy team thinks that it's a good idea to buy a gem and kill your Riki player friend, just Doom the gem carrier and they won't see Riki coming!
Even if they function is identical ("silence" things from usage), Orchid (as any other silence) blocks only active skills, while Mute (see:doom) stops almost all passives (both skill and item based) from working opening much bigger opportunity for use (everyone hates Void, right? Ever tried Dooming him? No bash, no backtrack, he is basically melee creep, while Orchid'ing him will only give a post-silence-damage-boost-if-he-actually-didn't-backtracked-all-your-hits-lol-ltp-noob-cyka)