More often than not, bionic human and human-cyborg are used interchangeably, simply because both refer to any individual that has any kind of artificial replacement of any part of its body. The fact that both are used interchangeably does not mean they are the same, although it can be very hard to differentiate between the two accurately.
A human-cyborg is someone that has some kind of integrated abilities or some kind of artificial replacement that is interacting directly with the person's brain in such a way that they can change the way it functions. A bionic human, on the other hand, is someone who has a part of his body replaced with a kind of technology or robotic hardware in order to increase the functionality of the body or the replaced body part. Human cyborg can also be regarded as a bionic human, but a bionic human is never a Human cyborg.
As their names and descriptions suggest, both bionic humans and human cyborgs are humans at the core. Both have alterations to their body. The difference in those alterations is what makes a bionic human and human-cyborg stand apart. A bionic human is a human who has had a limb replaced by a mechanical device.
An example of this is a person who may have a robotic leg or arm. They might also have a mechanical heart. A cyborg has an alternation to the brain. For example, parts of their brain may be replaced by an electronic or computer-based interface.