Center panned audio removal is commonly known as "vocal removal" or "karaoke mode" and is when identical elements in both the left and right channel are used to cancel each other out. Since vocals are almost always panned in the dead center, center panned audio removal almost always removes vocals close to 100%.
Non-center panned audio removal on the other hand isn't removing the left channel, or removing the right channel. Rather, with non-center panned audio removal, you figure out what IS in the center, then subtract the center from the left channel and subtract the center from the right channel.
Non-center panned audio removal differs from shifting the sound stage. Shifting the sound stage can be used effectively with either center panned audio removal or with non-center panned audio removal. While (non-)center panned audio removal and sound stage shifting work together to deliver superior results, they are not the same thing. Sound stage shifting is remixing the playback of the left and right audio channels.
Typically, center panned audio removal is used with vocals and bass parts of songs. Other instruments are often panned slightly left or right. In these cases, instead of shifting the sound stage while using center panned audio removal, it may be easier to use non-center panned audio removal instead.
Depending on what instruments you wish to filter out of a song, center vs. non-center panned audio removal provides two different starting points to make the task easier.
For more information about center-panned audio removal, see Removing Vocals from Songs.