Cloud can be defined as computing resources that are remote to you and you can use them by your internet connection you use at home or work. Definitely you don't have to buy them and own them but you just get to use them and usually by paying a monthly fee to the providers own those resources. It's nice to be called in this way because are services far away from you, you don't need to know much about them and how they work although you have every right to ask and learn how services are running behind the curtains.
Online backup is definitely an expressions having the same meaning. To backup a business on cloud means to securely send the business data to remote secure locations through your company internet connection.
Usually a backup software will be installed to a server or to a computer that will first compress the selected data to backup, encrypt them and send them to the remote location securely.
Once the worst is happen, the company can recover its data to the primary location or to any other location they choose to do so.
The concept of cloud is not really new for some key players of the Data backup market. On 70's and 80's we had the service bureaus that were literally doing what's happening today; moving data,protecting them from where they were kept offsite to more secure locations. This concept is around the last three years now but in the old days the concept of cloud was called Tell-vaulting or electronic vaulting that in the end of the day the concept was the same through the available technologies of that era.
A lot of people have still difficulties to grasp and understand the tiny technological powerful word of cloud that popped up three years ago and changed literally our lives since are used to keep their data on their computers and they have that fear now where are their files stored. One of the key players of Tell-Vaulting on Canada have seen this concept on its early form and it specializes on backup for disaster recovery for 26 years now.