There is a difference in the length of regular stocks and collapsible stocks buffer assemblies. The lenght of the buffer tube and the length of the buffers should have been obvious to you. Full length stocks have a longer buffer tube and buffer.
The CAR buffer should be used with the CAR stock. The recomended Buffer for 9mm and a CAR stock is heavier than the 223 CAR buffer. Some rifles have functioning problems when using the lighter CAR buffer. Also use the CAR spring in CAR stocks and rifle spring in full length stocks.
When I did a 9mm carbine with the CAR stock, I used the RRA recomended 9mm buffer and have had zero malfunctions. I did not try the standard CAR buffer so I can not tell you if it would have worked or not. Some people suggest an even heavier buffer than the RRA 9mm one but I don't know where they get them.
The standard rifle buffer seems to work fine with the 9mm when used with the full length stock.
This information is what I have read and done so far
I will add that there is a post on here titled "9mm buffers for dummies" and it gives a quick overview to what I was trying to say. The standard CAR buffer allows the bolt to open a little early . This may or may not cause functioning problems but some people also say that it batters your lower more.