Wheelbarrows are usually used in construction or landscaping, while garden carts can be used to move dirt around. Garden carts also come with a variety of different attachments that allow you to use them as a work surface, tool tray, and more.
A wheelbarrow is designed for heavier materials like concrete or asphalt, whereas a garden cart is lighter and better suited for things like moving dirt or composting material. Wheelbarrows require more strength than most people have at home, so they're not often recommended unless you happen to work with heavy loads regularly (e.g., construction). Garden carts are easier for the average person but may lack some stability if pushed too hard over a rough surface.