There's a very slight difference. Search is "looking for", while find means "discover". It can be grossly translated as "try and find", as "search" does not hold the same signifiance, and does not automatically means success. "Find", on another hand, means that Remilia is expecting success. If she just said "Search", then Sakuya could just look around, and say "it's done, I searched", while if Remilia says "Find", then Sakuya is forced to try until she finds Patchy.
Actually, what Remilia says is "search Patchouli (who went missing)". The part in the brackets is implied by the word she uses. Because it´s an order, I felt that just "search her" didn´t sound strong enough so I added a "find" to it.
Third, kill the culprit of this abnormal phenomenon.Understood, mademoiselle.... What should I do if all three orders can be carried out at once?Sakuya is really asking, "What if the culprit is Patchouli-sama?"Second, solve the mystery about this abnormal phenomenon before the Scarlet Devil Mansion is completely frozen up.I leave that to you.Sakuya. I now give you three orders. Please listen carefully.First, search for and find Patchouli Knowledge....That is all.... Understood.In any case, we don't need a Yôkai or whatever else causes such an annoying unnatural phenomenon here (in the Scarlet Devil Mansion).Humans with blood flowing through their veins are strong against the cold, right? I'm expecting results, Sakuya.