Biodiesel vs. "regular" diesel

 I met a friend yesterday who asked me what is the difference between regular diesel and bio diesel. Since it function the same way in a motor, he could not see any difference. I tried to explain and told him about what is perhaps best known, that regular diesel is based on fossil oil and that the carbon dioxide that comes from it increases the carbon dioxide content in the air.
The carbon dioxide of bio diesel, on the other hand, is renewable and in a cycle with a shorter circulation of carbon dioxide. I also said that it is less harmful, but it's not correct. It's just as harmful as the usual diesel in terms of impact on climate change. The difference is if you use a waste such as fish offal, you can reduce the use of fossil diesel and thus reduce these emissions.
But the question remained with my acquaintance that what's really the difference? My final answer was that the difference between bio diesel and ordinary diesel is how the hydrocarbon molecules are built. In fossil diesel, it basically consists of carbon and hydrogen, on average, the chemical formula C12H24, while bio diesel is a fatty acid ester that also contains oxygen and has a chemical formula that looks like this; C12H24CO2CH3.
The difference affects energy content, density and much else which I will not address here.