Does a player get the same amount of Activity Points for biking, walking, or running over identical distances?

Players do not get Activity Points based on distance, except as it affects the duration of the activity.

Activity Points will certainly be different for biking, walking, running, and any other activity as they have different intensities of movement, among other reasons. 

Additionally, where the Pod is worn may impact the amount of Activity Points generated, especially, for example, in the case of biking, where the wrist is relatively stable, but ankles may be constantly in motion.