Don't confuse backup software with the drive itself. As noted in the article, the G-Drive Slim does not include backup software so that must either be part of the PC's operating system or was added later.
A dedicated backup drive is not necessary but may be the best option with some backup software. There are lots of devices that can be used for backups. Those include but are not limited to:
1. dedicated internal drive
2. dedicated external drive
3. network connected drive
4. other devices such as a flash drives
5. the cloud (internet connected storage)
6. a NAS device (network connected file server)
7. more than one of the above.
If the drive on the other PC is shared on the network and that PC is always on, that drive could be used. There would be no need for a new drive. I suggest using more than one backup device with the second one preferably being at another site. That could be on a device stored at another location or internet connected storage.
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Cloud and other offsite storage backups should be encrypted for privacy reasons. That requires backup software that supports encryption.
A flash drive can be left plugged in 24/7. The biggest issues with flash drives are speed and short lifespan if used heavily. I don't trust flash drives for heavy use applications such as continuous or daily backups.