Here are some difference between Roomba 630 and 655.
Roomba 630 vs 655
images from manufacturer

As far as I know, the Roomba 655 is a Costco model whereas the 630 is a general model that you can buy from official site http://store.irobot.com and other online shopping malls such as Amazon.com and Walmart.com

Scheduling Feature
Both of them belong to the Roomba 600 series, however, the Roomba 630 has no scheduling function while 655 features On-board Scheduling that allows users to preset cleaning times.

Battery
The 655 uses the purple iRobot XLife Extended Life Battery doubles the cleaning cycles of the yellow iRobot Advanced Power System battery which is used on the 630.

More:
* According to iRobot, the 655 also comes with a redesigned side brush that cleans better and easier to remove.

* The 655 has the Dual Voltage Integrated Home Base whereas the 630 uses the Home Base (110V) and regular battery Charger.

* The 655 comes with 2 brush cleaning tools (1 round and 1 flat), 1 extra side brush, 1 extra rubber brush, 1 extra bristle brush, 2 C batteries for Virtual Wall whereas the 630 has only the flat brush cleaning tool, No extra brushes, no batteries for Virtual Wall.

P.S.
Both of them do NOT support Lighthouse that helps Roomba navigate room-to-room.

If you know other difference between Roomba 655 and 630, please share below to help others buy the right one.