On the Wii version, and on TPHD with 3rd person aiming (hence the name), it's possible to shoot the clawshot through solid walls. If the clawshot contacts something clawshottable on the other side of the wall, Link will clip through it directly, allowing for some skips and sequence breaks. This is not possible on GCN. This page will be covering the details of the technique on Wii specifically, although so far, every known implementation of 3pcc that's possible on Wii seems to also be possible on HD and vice-versa.
This works with both the regular clawshot and the double clawshots. While most clips require Link to be exactly up against a wall, some of them have a bit of leniency, where there can be a small amount of space between Link and the wall. If the clawshot successfully shoots through, the trajectory of the clawshot seems to be slightly exaggerated based on the height that the clawshot was released at. For example, if you clawshot through a wall a small amount above the center of the screen, the clawshot will act as if it was shot upwards at a ~45 degree angle. If you clawshot near the top of the screen, the clawshot will act if it was shot nearly directly upwards. The reverse is true in the opposite direction.
These refer to 3pcc-ing to targets far above or below Link. Since it requires a "flick" to move the cursor quickly, this subset of 3pccs seems to only be possible with pointer controls enabled. Position Link directly against a wall. Pull the clawshot on the side of the screen, since pulling it in the middle will push Link away from the wall. While still holding B, aim near the center of the screen. Then, flick upwards (or downwards), and then release B to clawshot once the cursor is near the edge of the screen. The flick needs to be somewhat aggressive, but not overly so. Too slow of a flick, and the clawshot will clank the wall. There seems to be no such thing as "too quick" of a flick in theory, but the more aggressive the flick, the harder it is to aim accurately. Because of this, it's recommended to flick as softly as possible while still being the minimum speed to shoot through the wall. The video below demonstrates a vertical 3pcc.
These refer to 3pcc-ing to targets that are not too far above or below Link. These don't require a flick at all, and thus are possible with or without pointer controls enabled (although, they don't seem to work exactly the same, thus usually needing different setups). Position Link directly against a wall, and then angle Link some amount away from the wall (about 30 to 45 degrees from perpendicular). If you aim in the vicinity of where Link's head is, the clawshot should shoot through the wall without having to flick. The video below demonstrates a horizontal 3pcc.
Example with pointer controls disabled