Quote from logic_man:
I would say that traders tend to be more analytical and quantitative. Esoteric questions about statistical distributions don't really ever matter to entrepreneurs, but they may matter greatly to traders.
+1
Having done both, trading is much more about study and practice, and then you vs the market. If you like research, from college or whenever, you'll love trading.
Being an entrepreneur does involve solid research about your business area and preparation, but also involves many other areas. You've got to deal with employees, customers, laws, cities, payroll, rent, a bad economy, competition, independent contractors, etc. In my opinion, an entrepreneur has to keep track of many more moving parts in order to be successful.
Both are very risky; there are some business areas that are safer than trading, but they don't have the same upside. Businesses that have big upsides have the requisite risk.