We have just provisioned a carrier to provide us with an OC12 (622mbps) connection. The carrier asked if I wanted a Sonet or GigE handoff? What does the carrier mean by this and is there a difference?
It's not a limitation, it's providing the correct interface and signaling.
A copper cable with an RJ45-looking connector can have voice, any of several flavors of Ethernet, Token Ring, CDDI, T1, DDS56, ISDN ...
Optical is the same way; it can carry different types of signaling. The carrier is only asking your preference (so you can match it to whatever interface you have / desire).
IMO, GigE would be the better choice; it's a less expensive interface to buy (usually), and OC12 is going to max-out at 622Mbps.
You'll still get ~622 Mbps from the GigE, but you have some room to grow with just a little keyboard work (i.e., no new hardware required).