First let's start with Ben Graham's definition of investors and speculators.
Graham first stated that an investment operation is one which, upon thorough analysis, promises safety of principal and an adequate return and operations not meeting these requirements are speculative.
So an investor focuses on analysis to look for capital safety and adequate return. This is usually interpreted as fundamental analysis of the company, its business model, its competitive advantage, margins, sales growth and of course, the financials: cash on hand, debt, bankruptcy risk, capex needs etc.
Anything less of such analysis means speculation. A speculator is simply one that doesn't do that kind of rigorous analysis.
For me I think it's about different focuses.
An investor focuses on value.
A trader focuses on price.
An investor is interested in the value of a stock (or any other thing he wants to buy), and he spends an awful lot of time and effort to figure out this value (or intrinsic value). This is analogous to Graham's analysis. Or more accurately rigorous fundamental analysis of business operations and financials. Price serves only to tell him how much he actually has to pay if he were to buy the stock. Needless to say, the lesser the better. Graham and most value investors advocate buying 30-40% (margin of safety) below the stock's intrinsic value.
To an investor, profit is made when the stock price subsequently rises to its value which usually take years.
A trader is interested in the price of a stock and he spends an awful lot of time and effort following how the price has moved. Actual value of a stock basically serves no purpose for the trader.
To a trader, profit is made when the stock rises above his buying price and he sells it to another person willing to buy at a higher price. Usually also known as the Greater Fool.
So, that's that! Just two different philosophies here to make money.