Hello,
The Cloud version of DMS service is fully managed by Microsoft. Where as with Hybrid DMS, you need to have a server that can host the Hybrid DMS worker in the on-premises network. In the case of Hybrid- DMS, you still need to create DMS service in the cloud, but the cloud DMS will only be used for managing, orchestrating and status monitoring your migration pipelines. The actual migration tasks are executed by Hybrid worker that includes the backup file validation, upload to to Blob storage , calling the restore onto the target MI and final cutover.
With Cloud DMS, you need to have a site-site connectivity (ExpressRoute or VPN) between your on-prem and Azure networks, but with Hybrid DMS, you don't have to, the file uploads happen through the public internet. You don't have to worry about opening SQL Server port and SMB ports at Azure NSG. Hope this helps. Please let us know if you need more info.