A train conductor is the person who takes tickets, shouts "All aboard!" and might control the engine, while a musical conductor is the one who leads an orchestra. Same job title — not the same person.
From the Latin root conducere, meaning "bring together," a conductor does just that. A music conductor makes sure all the musicians come in at the right time and tempo, and a train conductor brings together all of the passengers. Another type of conductor is something that passes on electricity or heat, like a metal spoon, a conductor of heat when left in a pot that's simmering on the stove.