The Sony Lithium-ion NP-FG1 and NP-BG1 battery packs have roughly the same specs:
Dimensions (approximate): W 35.5 x H 8.3 x D 41.6mm / W 1.40 x H 0.33 x D 1.64 in.
Weight: Approximately 27g / 0.95 oz. (NP-FG1) / 26.8g / 0.95 oz. (NP-BG1).
Voltage / Power Capacity: 3.6V/3.4Wh (960mAh).
The only difference between the two packs is NP-FG1 allows the camera to display the remaining battery life in actual minutes, while the NP-BG1 merely shows a simple indicator.
Sony Style Canada has the following blurb on the NPFG1:
Give your Cyber-shot Digital Camera an extra kick with the NPFG1 InfoLITHIUM rechargeable battery pack. The NPFG1 features Lithium-ion technology which ensures maximum battery life and maximum power. It’s also quick charging, so you’ll spend less time waiting and more time taking pictures. Only genuine InfoLITHIUM batteries reliably show you exactly how many minutes of power are left, so you’ll never have to worry about unexpectedly running out of charge.