Sometimes they seem far apart, sometimes their philosophies seem rather similar. But historically, the Democratic and the Republican parties have demonstrated a fundamental difference in how they deal with economic issues (or don't).
Generally speaking, the Republican Party is considered business-friendly, as it favors limited government regulation of the economy. This includes restrictions that might seek to dimunize the pursuit of profits in favor of environmental concerns, labor union interests, healthcare benefits and retirement payouts. Given this more pro-business bias, Republicans tend to receive support from business owners and investment capitalists, as opposed to the labor component that constitutes workers and their interests.
Democrats are said to rely more heavily on government intervention to influence the economy's direction and keep the profit motive of businesses more at bay – subscribing to a belief that businesses are more focused on earning a return for shareholders and willing to cut corners in terms of protecting the overall social good. Higher regulation comes with increased costs, which Democrats believe in supporting through higher taxation. As a result, the party's approach is often described as "tax and spend."
During economic downturns, Democrats will, therefore, tend to believe that deficit spending is necessary to help stimulate the economy until private business prospects improve. They might also look to enhance and extend welfare programs to help citizens that have lost their jobs or are more in need due to more challenging economic conditions. Republicans would tend to rely less on government intervention, but might seek to alter the money supply. Lowering the Federal funds rate and the banking reserve ratios qualify as monetary policy levers they can pull.
The reality is that the lines between what are considered traditional Republican and Democratic approaches to regulating the economy are more blurred. The U.S. has run a budget deficit for nearly three decades, meaning it has spent more than it has taken in. This has increased the role of government in the economy and has meant that spending has continued in good times or bad, and under both parties' administrations.
Government politicians also have personal differences in how they manage the economy, of course. Still, knowing their party affiliation can still be a solid indicator in the approach they may take in influencing the economy.