A backup is a copy of your data that you can restore from. Disaster recovery is a standby copy of your servers that you can switch to and keep working while the originals are repaired.
Backup: can we get it back?
A backup protects the data. If a file is deleted, a server fails or ransomware hits, you restore from the copy. Restoring a whole server from backup can take hours or days, depending on its size.
Disaster recovery: how long are we down?
Disaster recovery protects the working day. A copy of your servers is kept ready to run somewhere else. If your office or main systems are out, you switch to the standby and carry on.
Disaster Recovery as a Service (DRaaS) means a provider hosts and runs that standby for you.
Do you need both?
Most businesses do. Backup without disaster recovery means you will get your data back but may be closed while you wait. Disaster recovery without good backups means you can keep working but may not be able to go back to a clean point in time.
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