Brag:
* Usually implies a more casual and informal tone.
* Often refers to exaggerating one's accomplishments or importance.
* Can be seen as arrogant or self-important.
Boast:
* Has a more formal and serious tone.
* Often refers to proudly proclaiming one's achievements.
* Can be seen as confident or even arrogant.
In essence:
* Bragging is often seen as more annoying or self-centered, while boasting can be perceived as more confident and impressive, though still potentially arrogant.
However, the difference is often very subtle, and both words can be used interchangeably in many contexts.