Crostini is Google's name for a new method of delivering native Linux applications on (some) Chrome OS devices. Crostini lets users access and run Linux apps from a container inside a special VM.
Recently, CloudReady v64 brought some similar functionality in the form of flatpak support. Flatpaks are Linux apps that have been specially packaged to include all dependencies, making them simple to install across a variety of Linux systems.
You may wonder, with such similar goals, why there would be two solutions at all or how they differ. The primary difference is ease of use. Crostini asks users to install apps from a command line, where they need to understand how to use a Linux package manager and deal dependencies. Contrastingly, on CloudReady flatpaks can be installed with a simple download and double click, meaning anyone can try them regardless of experience.
Some components, like "sommelier", are used by both, and Neverware will definitely continue to watch how Crostini is being built to consider aligning them more or enabling both as options.