There isn't much of a difference between the Galaxy S7 and S7 Edge. They are almost identical in almost all the areas like hardware, camera and processor.
Look and feel
The dimensions read 142.4mm x 69.6 mm x 7.9 mm for the Galaxy S7, while the physical dimensions read 150.9mm x 72.6 mm x 7.7 mm for Galaxy S7 Edge. The S7 tilts the scales at 152 grams while the S7 Edge will weigh 157 grams.
Color availability for S7 is Dark Grey or Gold and for S7 Edge, the device is available in Dark Grey, Silver, or Gold.
Display and battery
The screen size is where the devices differ. The S7 has a 5.1 inch display at a pixel density of 577 ppi. The S7 Edge comes with a 5.5 inch display at a pixel density of 534 ppi.
Both the devices share the same Super AMOLED display at qHD resolution. But, the screen has a curved edge display.
The battery differs between the two devices - the S7 has a 3000 mAh battery and S7 Edge features a 3600 mAh battery. The battery backup will not differ much between two phones as the battery needs more power on the S7 Edge.
Apart from what has been stated above, all other features stay same across both the devices in all other aspects.