Some of those terms are misleading. For example, server-free backup is not server-free; it has to have a server, or its equivalent, somewhere to manage the process.
However, literalism isn't the point. The question for you is, which one of these "free" backup architectures is best for your storage set-up?
The idea behind all those backups is that they take all -- or most -- of the load off some of the components in your system. Depending on your environment, this can be a considerable advantage for you as an administrator, even considering the extra hardware some of those backup approaches require.
LAN-free backup is backup that is done not over the LAN but either over the SAN or with a tape device directly attached to the storage subsystem, such as a RAID array. You might want to try this approach if you don't want to add to the load on your LAN and if all your storage is either connected to a SAN or concentrated in a few arrays. This approach is a popular alternative for systems with network-attached storage (NAS) filers.
In the case of server-free backup, the backup task is accomplished without the use of the server. The backup process is managed elsewhere in the system, often by software running on a switch in the SAN. This keeps the load off the server. However, preventing a single point of failure requires special consideration, because if something happens to the SAN, not only will you lose your ability to perform backup, but your ability to do a restore may also be severely compromised.
SAN-free backup refers to an architecture that doesn't use the SAN in the backup system. This could mean that backups are handled over the LAN, but more commonly it refers to a direct-attached storage backup where the backup is connected directly to the storage array. This approach is most popular in highly centralized storage architectures where almost all of the storage is concentrated in a data center where trained administrators watch over everything.
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About the author: Rick Cook has been writing about mass storage since the days when the term meant an 80 K floppy disk. For the past 20 years he has concentrated on issues related to storage and storage management.