The first verb I learned to mean "to drop" was 落{お}とす (otosu) as the transitive form of the verb 落{お}ちる (ochiru) (which means "to fall"). But recently I met the verb 失{うしな}う (ushinau) which according to Jisho.org is also transitive and means "to lose; to part with", which for me ends up being equivalent to "to drop". And while searching about this, the verb 無{な}くす (nakusu) also showed up in my search, and according to Jisho.org it also means "to lose something", which at the first glance I thought to be intransitive, but again Jisho says it is transitive.
In short: It looks like 落{お}とす (otosu), 失{うしな}う (ushinau) and 無{な}くす (nakusu) are all transitive and mean "to drop". What are the differences between them?