To 'bury the hatchet' means to bring about peace between two opposing sides or parties. It goes back to the Native American custom where opposing sides placed a tomahawk on the ground to declare a truce.
When we 'steal someone's thunder' it seems purely metaphorical: either diverting attention away from someone who perhaps deserves it or to lessen someone's authority. However, the idiom does have more literal beginnings. John Dennis was a (largely unsuccessful) playwright who invented a machine to make the sound of thunder for his plays. Disasterously, the play which the machine was made for closed early due to poor attendance. The play which followed Dennis's used the same thunder machine which has been left backstage. Dennis, who was apparently in the audience, stood up and declared 'By Jove! They've stolen my thunder!' and the idiom has stuck ever since.