It's certainly both. The genetic component is clearest to me when I see kids grow up in the same household and have differing levels of patience and impulse control from a young age. Then, people tend to become less impulsive as they age through both biological and deliberate means.

The degree to which impulsiveness can be directly reduced is an interesting question. I think a big part of the human condition is a frustration with one's impulsivity, and I suspect that that's driving the surge in adult ADHD diagnoses in some countries.