There is a some difference in the meanings I am accustomed to:
An impulse is an immediate urge, a desire to do something right now. An example (for a woman) is an urge to buy a beautiful pair of shoes she sees. Most people get these urges, but almost always resist the urge (don't buy the shoes). Someone who often has these urges, and frequently gives in to the impulse (buys the shoes) is impulsive.
Someone who is impetuous is impatient, makes fast decisions, or easily makes big changes in areas like career, schooling, relationships (non-trivial areas). Here "fast" is relative. In changing career fields, it would be "fast" to do it after thinking about it for only 2 days, or to make a second change in the same year. For much smaller decisions, "fast" might mean deciding something in 20 seconds, that most people would think about for an hour before deciding.