Hi Thomas,
OneDrive for Business and OneDrive are cloud services. Users can store files to them which will be saved in the cloud. So they can access the files in almost anywhere with almost devices if there is internet connection. Meanwhile, we can use the sync client of OneDrive for Business to sync these files from cloud to a local synced folder. The sync client will sync the changes between cloud and local synced folder. When user cannot connect to internet, they can modify the local synced files. After connecting to internet, the changes will automatically be synced to cloud. Below are two articles for your reference:
What is OneDrive for Business?
Shared drive
If you mean network drive, this is a storage device on a local access network. We can store and share files with network drive. However, we cannot access it in anywhere with other devices. We only can access the files through the local network. When you outside of your office or home, you cannot manage those files anymore.
Best regards,
Tim