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Can someone explain to me what exactly local time machine is? Does it just apply to Versions? Or is it a system wide thing that could be used to restore a deleted file etc?
Here is info from the TM help section. Local snapshots are mainly used on laptops. They do not have anything to do with versions.
Time Machine overview
When you connect your computer to a new disk, a message appears asking if youd like to use the disk to back up your files. Use this information to respond to the message.
Use as Backup Disk: Time Machine will use this disk for backups. Initially, Time Machine makes a complete backup, including system files, applications, accounts, preferences, music, photos, documentseverything you keep on your computer, except for a few temporary files (such as web browser caches).
Depending on how many items youre backing up, your initial backup could take a while. Subsequent backups take less time because only items that have changed are backed up. You can use your computer during backups.
Time Machine works best if you use your backup disk only for backups. If you keep files on your backup disk, Time Machine wont back up those files, and the space available for Time Machine backups is reduced.
Encrypt backup disk: For security, select this checkbox. If you back up to an external disk and do not encrypt the backup disk, any person who gains possession of the disk can read the information on it.
Decide Later: Time Machine will display the message again each time you connect to the disk.
Dont Use: Time Machine will not ask again if you want to use this disk for backups.
If your computer is in sleep or your backup disk isnt available when its time for a scheduled backup, the backup is not performed. Backups resume after the computer and backup disk are available again.
If you have a portable computer, in addition to saving backups on your backup disk, Time Machine saves hourly snapshots of files and stores the snapshots on your computers internal drive. If your backup disk isnt connected, Time Machine continues saving snapshots on your internal drive, and then resumes backing up to your backup disk when you reconnect it.