Pedantically, any storage of money is a bet, because it could change in value. However, to the Buffett-style investor, you think about whether you want to buy the entire company, even if you can only afford one billionth of it. You look at a reasonable projection of earnings growth--and don't buy companies that are unpredictable (like early stage tech companies). You try to buy at a discount ("margin of safety") in case you are wrong in some fashion. And so forth.
So for example, Coca-Cola (KO) is pretty predictable. Absent any major blunders by management, KO is going to grow roughly the size of the economy, and it's going to put out 3% a year in dividends. So the fair market price of KO is reasonably determinable, and you wait until you can buy it at or less than it's fair price.
This is usually contrasted against technical traders, momentum traders, etc., who are not investing in the fundamentals of the business and assuming the price will follow good fundamentals, but rather they are betting on how the price will change.
So "investing" is seen as buying fundamentals and "betting" (or "gambling") is seen as buying on expected price changes.