See I thought a conductor was a person who grabs a live main wire while standing in water.

In the US, a conductor is the one who checks tickets, makes announcements, and delegates tasks to the crew to help ensure things keep moving on time.

The locomotive engineer is the one who is “driving” the train. They run the engine and communicate with dispatch and traffic control to keep them informed where this particular train is fitting into the overall juggling act,. They also make every effort to keep things safe (watching for signals, obstructions, etc.).

I’m not 100% sure if the terminology is different outside of the Us.

(Source: My father is a 3rd generation locomotive engineer.)

In the railway context an engineer was the person who worked the engine.

In German the word comes from Latin roughly meaning inventor. Presumably the general usage of the word engineer in English has the same etymology.