One essential difference is the information available. A person who trades securities makes use of economic data, corporate business performance metrics, news, and technical analysis, and the access to relevant information is strictly regulated.
When betting on the outcome of unpredictable events such as sports results, luck and randomness play a much bigger role depending on the type of game involved. Statistics and analytics nonetheless can influence sports betting behavior. If you find out, for example, that a football club’s best player is injured, you have better odds of winning if you bet on a victory by the opposing team.
Mathematical models also get utilized in games of chance, but their informative value is limited in this setting. In the game of roulette, for example, the probability of red or black winning on the next spin still amounts to around 50% even if red previously came up ten times in a row.
There, of course, are investors who also follow their gut instincts or even employ methods like astrology. In principle, though, trading relies much more on systematic research and strategic reasoning.
That has a lot to do with how prices and odds come into being in the first place.