Both services have different ways to reduce storage on local drives.
Cloud storage is a great way to expand unlimited hard disks or SSD space on your computer to locations that can be reached by the internet. Many services combine synchronization and disassembly of storage. Synchronization ensures that files on each linked device are stored in a central repository and are copied and updated on every attached device. Storage offloading allows you to choose to save the file in central storage but not at each endpoint after the file was first uploaded.
Dropbox and iCloud Drive are two popular options for macOS, iOS and iPadOS cloud storage, and they differ substantially in this approach. Dropbox changed its approach last summer for a personal account, so it might be a little different from what you remember if you haven’t used it for a while.
iCloud Drive works with all iCloud storage tiers, though you can only really use it at 200GB or higher tier. macOS fully manages which files are stored on your Mac, and which are cleaned to free up storage, and only when you have Optimized Mac Storage are checked in the iCloud preference panel (macOS Mojave and earlier) or in the iCloud tab of the Apple ID panel preference (macOS Catalina). You can also check Desktop & Document Folders to synchronize and optimize those folders across Macs.
iCloud Drive can be set to clean local files that are rarely used and keep them in the cloud by checking the optimization settings.
macOS uses various gestures about file access and modification to remove the least used from each Mac with the settings enabled. The files are always stored in iCloud, and can be reached via the Files application on iOS and iPadOS or iCloud Drive via iCloud.com.
With Dropbox, the Dropbox folder on every Mac that you use automatically synchronizes and updates everything from all other Dropbox sources on all platforms and through Dropbox.com. You can Control-click any file or folder in the Finder, and select Smart Sync> Online Only to move files or folders and nested content from the current Mac. (A paid Dropbox package is required.)