Doctors, what is the difference between vegetarian fish oil and regular fish oil supplement?

No such thing: 'Vegetarian fish oil' is synthetic, made in a chemistry lab, which makes it 'okay for vegans' who don't have an aversion to 'chemicals.' Whoever you decide to believe about fish oil supplements (the last three big studies showed no cardiac benefit), they're no substitute for healthy eating, avoiding smoking, and staying physically fit.