Vector and bitmap images differ in how they store and represent graphical data. Bitmap images store data as a grid of pixels and cannot be resized without quality loss, while vector images use mathematical expressions to store geometric shapes and lines and can be resized without quality loss. Common bitmap formats include JPEG, PNG, and GIF, which are resolution dependent, while vector images are resolution independent. Popular programs for creating and editing bitmap images include Paint and Photoshop, which offer different price points and complexity levels.