* A833 4-speed: This was a common, robust 4-speed manual transmission found in many high-performance Challengers.
* A904 3-speed automatic: While not a stick shift, it's important to note that a 3-speed automatic *was* available and often confused with manual transmissions in general conversation about classic cars.
Therefore, there's no single name like "Type X" for the stick shift. The A833 4-speed is the most likely candidate if you're talking about a manual transmission in a 1970 Dodge Challenger.