To expand on Hand-E-Food's answer.
A backup is a complete snapshot off your device at that particular point in the time the backup is made. Not every synchronize causes a backup, and the backup does not contain actual copies of the Apps, Music, Books or Photos stored on your phone. It does however contain all the settings, contacts, calendars, saved games and anything else not handled by the synchronize.
A synchronise copies all Apps, Music, Books and Photos to the phone, and works in conjunction with the backup. When you restore a backup, it will require you to synchronize to retrieve the actual Apps etc.
You can synchronize your phone irrelevant of the backup state, and if you don't restore a back after a reset, you can continue synchronizing items the way you did before the reset, however all your application settings, saved games etc. will be lost and has to be reconfigured and restarted.
Yes, the two models are physically different. The radio is different.
As per Apple's website, the radio frequencies aren't the same. The verizon iPad supports Verizon LTE, and as per this post, AT&T 3G. However, the Verizon iPad does not support all LTE frequencies that the AT&T iPad does.
From Apple.com:
Wi-Fi + 4G for AT&T model: 4G LTE (700, 2100 MHz); UMTS/HSPA/HSPA+/DC-HSDPA (850, 900, 1900, 2100 MHz); GSM/EDGE (850, 900, 1800, 1900 MHz)
Wi-Fi + 4G for Verizon model: 4G LTE (700 MHz); CDMA EV-DO Rev. A (800, 1900 MHz); UMTS/HSPA/HSPA+/DC-HSDPA (850, 900, 1900, 2100 MHz); GSM/EDGE (850, 900, 1800, 1900 MHz)
Notice that there are some differences between the listed frequencies. They're nearly the same, but not quite.
Edit:
To confirm, the difference is a hardware difference, not a software imposed limitation on AT&T LTE. From the Macrumors article:
The Verizon iPad hardware supports only the 700 MHz band for LTE to match the carrier's technology, while the GSM version sold for use on AT&T's network supports both the 700 MHz and 2100 MHz bands as used by that carrier.
If you're looking to travel internationally, go with the AT&T iPad. (I got the Verizon iPad because I wanted the free hotspot feature, which AT&T does not offer for free at this time.)
Best Answer
Huh! So I asked an Apple representative, but they didn't know. I also asked Sennheiser and they finally got back to me. Apparently the i300 are exclusive to Apple (as I suspected), and although they look very similar to the MM70i, they're apparently closer in sound performance to the cheaper MM30i.
So basically, the Apple exclusive Sennheiser i300 are equivalent to the Sennheiser MM30i.
You can see the MM30i here:
http://www.sennheiser.co.uk/uk/home_en.nsf/root/private_headsets_mobile_music_504739
According to the Sennheiser representative, the MM70i has a better bass response and more accessories than either the MM30i or the i300.
So, from what I can gather, it seems buying the cheaper MM30i, or the more expensive MM70i, is a better option than the Apple exclusive i300.
Update: Since I wrote this question, it appears that Apple have reduced the RRP of their i300 to match that of the MM30i. However, as Amazon seems to consistently offer a 30% discount on the MM30i's, the Apple exclusive headphones are still more expensive in a practical sense.