A chef's knife is a straight-edged knife with a belly that curves toward the point. Blade length varies from about 6 inches to 14 inches, but the typical length is 8 inches. This is an all-purpose knife in food preparation. It's used for everything from cutting large pieces of beef to chopping vegetables. It's also great for mincing, dicing, slicing, and more.
The utility knife has the same appearance and function as a chef's knife, but it's smaller and more versatile. The blade length is between 4 and 7 inches.
Before the rise of the chef's knife, this was the multipurpose knife that did pretty much everything in the kitchen. Now it's been mostly relegated to basic tasks like cutting pieces of meat or preparing small dishes.