Do you get tetanus from gangrene?

Possibly: The processes which produce gangrene imply the loss of nutrient blood supply to tissue thru infection triggered blood clots, frostbite, etc. As the skin begins to break down the open areas could be contaminated by tetanus spores & tetanus germs could contaminate that wound & produce tetanus. However, gangreen can exist without tetanus germs & have a variety of other germs that are just as deadly.

No but same genus: Great question and i used to get confused with this as well. However the genus clostridium has well over 60 species of bacteria that may cause different disease processes. Specifically, clostridium botulinum, clostidium perfringens and clostridium tetani will cause botulism, gas gangrene, and tetanus respectively.