My Understanding of TC4 is as follows.
TC4C is a standalone board with an Arduino (similar) and the TC4 Shield on one board.
HTC Plays along with TC4C it seems to me, and can be stacked on a TC4C or Connected with a cable?
TC4 Shield is a shield that stacks onto an Arduino Uno, or similar. (Separate Unit) Mega's work with 2 pins bent away. I2C I think?
HT Shield is a shield that stacks onto a regular TC4 Shield, which is stacked onto an Arduino (3 Units)
I have not done much research into the HT Shield, as I do not have a Hottop, so I have no need for the Hottop Boards. Miroslav would likely have more information for you about how the Hottop side of things works.
I will be getting 2 regular TC4 Shields, as I already have access to 2 Arduino Megas to put them on.