"The Sd.Kfz. 234 (Sonderkraftfahrzeug 234, Special Purpose Vehicle 234), was a family of armoured cars designed and built in Germany during World War II. The vehicles were lightly armoured, armed with a 20, 50 or 75 mm main gun, and powered by a Tatra V12 diesel engine. The Sd.Kfz. 234 broadly resembles the appearance of Sd.Kfz. 231 (8 rad)." (https://en.wikipedia.org/wiki/Sd.Kfz._234)
The 234 chassis is actually what we identify as the Puma. This model for example is identified as a "Pakwagen" with a 75mm PAK 40, while the 234/3 (as you say) was actually identified as the "Stummel" with a 75mm K51. You are referring to what civilians refer to as the "Puma" which is a post war name for the vehicle Sdkfz 234/2 with a 50mm gun mounted to the turret made for the Leopard Panzer. This turret on the 234/2 along with the whole of the 234/1 resembles other Aufklärungspanzer Sonderkraftfahrzeuge, during the war neither of these vehicles were called "The Puma". It is acceptable to call anything that uses the Sdk.Fz. 234 chassis system a "Puma".