1. Dependency Management: Composer is a dependency management tool for PHP, whereas Packagist is a repository for PHP packages. Composer allows developers to declare the libraries that their project depends on and manages the installation and updating of those libraries. Packagist is the default package repository for Composer, where developers can search for and find packages to include in their projects.

2. Installation and Usage: Composer is a command-line tool that is installed globally on the developer's machine, allowing them to use it for multiple projects. It requires a composer.json file in the project directory, which defines the dependencies and version constraints for the project. On the other hand, Packagist is accessed through Composer, where developers can search for packages using the command-line tool and add them to their composer.json file.

3. Package Management: Composer manages packages on a per-project basis, meaning that each project can have its own set of dependencies defined in its composer.json file. It installs the required packages in a vendor directory within the project, allowing for easy version control and isolation of dependencies. Packagist, on the other hand, is a centralized repository that contains packages contributed by the community, making it a one-stop-shop for PHP packages.

4. Version Constraints: Composer allows developers to specify version constraints for the dependencies in their composer.json file using semantic versioning or other methods. This provides flexibility in choosing which versions of a package to use and ensures compatibility with the rest of the project. Packagist, being a repository of packages, also provides version information for each package, allowing developers to choose the desired version when adding the package to their project.

5. Autoloading and Class Mapping: Composer provides autoloading functionality, which automatically loads the required classes from installed packages. It generates an autoloader file that can be included in the project, saving developers from manually including multiple files. Packagist, being a repository, does not directly handle autoloading but provides packages that are compatible with Composer's autoloading mechanism.

6. Package Distribution and Contribution: Composer allows developers to easily distribute their packages by publishing them to Packagist. It provides a standardized format for package distribution and allows for easy management of dependencies for other developers using the package. Packagist, being a repository, facilitates the contribution of packages to the PHP community by providing a platform for developers to share their packages with others.

In Summary, Composer is a dependency management tool that allows developers to define and manage their project dependencies, while Packagist is a repository that provides a vast collection of PHP packages that can be easily included in projects using Composer.