In a carbine length buffer tube, you can run any carbine length buffer in any weight you want and you can also choose to add a spacer/quarters to reduce bolt overtravel.
In a carbine length buffer tube, you can run a specialty, extended length, 9mm buffer (i.e. one that is longer than a standard carbine length buffer) that eliminates the need for a spacer/quarters because the buffer is longer - basically the equivalent length of a standard length carbine buffer and an overtravel reducing spacer/quarters.
In a rifle length buffer tube, you can run a rifle buffer and you can also choose to add a spacer/quarters to reduce bolt overtravel.
In a rifle length buffer tube, you can also run a standard carbine length buffer, but you must run a spacer to take up the difference in buffer length between the rifle and carbine lengths. This spacer is different than the overtravel reducing spacer/quarters which you can also add if you are running a carbine buffer and length spacer in a rifle tube. Basically, there are two different spacers at play here, but you could make one spacer that resolves the overall travel reduction necessary.
In a rifle length buffer tube or a non-standard length carbine tube, you can also run a specialty 9mm buffer, but you need to determine how much of a spacer you need to add to adjust for the difference to the length of the rifle or carbine buffer that you would normally run in a .223/5.56 setup and/or the additional spacer length necessary for any additional 9mm specific bolt overtravel reduction.
You cannot run a rifle length buffer in a carbine buffer tube, unless you modify the length of the rifle buffer so it will work.
There's so many magical, specialty buffers that it is very easy for people to get them confused as to whether they are just a heavier than standard weight, longer than standard length, or both.