A sound of thunder is used to represent the T-Rex steps and Travis’s gun. The two things that cause giant turns in the story.
The butterfly Eckels kills is easy—the butterfly effect. Also, butterflies represent freedom, a freedom he killed when his actions changed the outcome of the election.
The path they’re supposed to stay on is written destiny. It’s the path that needs to be taken in order to get back to their normal lives.
The bullets represent the disturbance of the past, and future, all at once.