Hey dg92104,
It has been quite confounding to sort out the tangled web of backup/sync systems on my Verizon SGS3 that I bought 2 months ago. I've asked Samsung, Verizon and Best Buy Mobile, and called Best Buy tech support, and none of them could tell me what was going on.
You don't mention it in your posts or profile but I am guessing your carrier is Verizon? I'm guessing because I believe
Backup Assistant Plus is a Verizon app and you have 500 mg of space on Verizon servers. (I say "I believe" because this is what the Verizon employee told me, but he was so perplexed by my inquiry that I have to qualify it.) The "Documents" that are backed up with BAP are only the Documents folder on the sdcard. Same for S Memo. I found an attachment from my email program saved online. If you press the menu button while in the Setup BAP section, you can access what has been saved, which seems to be only stuff on the sdcard, though I don't have Pictures and Music etc selected to backup. There is an option under "Account Settings" for "Allowed Applications" but the Modify option is greyed out and I can't see anyway to adjust this. I cannot see that this program is providing anything of use, except it may be backing up my contacts somewhere. The date for last back up of contacts is 1 week ago, though there is a manual back up button there.
Then there is the "
Back up and reset" selection under the Personal section of Settings. This claims to "Backup app data, Wi-Fi passwords, and other settings to Google servers." If I deselect the check mark, it wants to erase the data that has been saved. My Gmail address is used, but there is no indication if anything has ever been backed up here. (Maybe this is related to the "Google" account below?)
Then there is "
Email" under accounts. This claims to sync email and allows for configuration of syncing based on time, peak hours, etc ... I'm assuming it's only related to updating my inbox on my phone.
Then there is "
Google" under Accounts. Using my Gmail address, it claims to sync App Data, Calendar, Chrome, Contacts, Gmail, along with 9 other things. The date shows today's date as the last sync date, though I have no idea where this is going.
Then I have "
Samsung Account" under Accounts. This uses my other email address (as does BAP) and claims to sync Calendar, Contacts, Internet and S Memo, all with today's date as last synced. (I am currently not able to log into my "Profile" through the phone for some reason.) I have not been able to find anything saved on my Samsung account logging in through my computer and browser.
I also can sync manually from some apps - in S Memo I can do a sync and see it show up on Google Drive. However, with the stock Calendar app I synced it but it didn't show up on Google Drive, so I don't know where that's going.
I have synced with the Kies PC host program and have been able to back up and restore. S Memo files.
I did an online chat with Samsung support but that was pretty much a waste of time, as the person was apparently unable to understand me and I sure was unable to understand them. They did seem to say that the data could only be retrieved if I changed phones. I have not called Verizon Tech support, which would be the last effort from any so-called official source.
That's what I've been able to figure out so far.
Also, how did you conclude that the Sync toggle in notifications is a "one time" sync? I have no idea what that toggle relates to.
Edit: I just figured out that this toggle enables Settings>Data Usage, then Menu Button and "Auto sync data" is selected or deselected. I am still not sure what this means.
The manual that was delivered to me through the Samsung website has a number of things that don't coincide to my device. Perhaps it doesn't take into account Jelly Bean.
I have found these tools to be ridiculously confusing. Only with Kies do I know what is going on, though that's all manual.
And, what country are you in?
Update: The following thread has info pertaining to this thread. Claims are being made there about what does what but I'm still not seeing the evidence of these claims yet. http://androidforums.com/samsung-galaxy-s3/641695-email-doesnt-auto-sync-since-update-jellybean.html