Containers and virtual machines are fundamentally different, with Docker allowing users to select only the necessary components to build applications without unnecessary extras. Docker images consist of "layers," which optimize storage and efficiency by reusing components rather than downloading them anew each time, similar to adding toppings to an existing pizza rather than making a new one from scratch. This layering concept is facilitated by the "copy-on-write" system, which allows for resource sharing unless a base image is significantly altered, thus saving storage space and time during image pulls and pushes. Codefresh, being Docker-native, leverages caching these layers to expedite builds, offering a more efficient alternative to traditional continuous integration methods.