The conductor walks along the carriage of a moving train. Are the trajectories of its motion relative to the train and relative to the Earth the same?

the trajectories are the same if he does not go back and forth, but goes in one direction.

Remember: The process of learning a person lasts a lifetime. The value of the same knowledge for different people may be different, it is determined by their individual characteristics and needs. Therefore, knowledge is always needed at any age and position.