Managed versus unmanaged packages
Key Takeaway
A managed package is locked, but its provider can upgrade it and push the changes to your org. An unmanaged package is yours to edit but can't be upgraded, so to get a newer version you uninstall it and reinstall the new version from AppExchange.
A package is a container that a provider uses to deliver apps, tabs, objects and other components into other Salesforce orgs, often through AppExchange. Packages are either managed or unmanaged. The type decides whether you can edit what you install, how upgrades reach you and whether the contents count against your limits.
What a package can hold and who chooses its type
A package can be as small as one component or as large as a set of related apps. Its provider can distribute it to other Salesforce orgs, including orgs outside the provider's own company.
The provider chooses whether a package is managed or unmanaged, not the admin who installs it. That type then controls how the solution behaves in your org.