This is NOT suppose to be a complete explanation of everything related to bit depth and channels, it's only an explanation of the bit depths in photoshop in relation to each other!
Remember, 8 bit, 16 bit, and 32 bit images are NUMBER OF BITS PER CHANNEL! There are basically 3 channels in an RGB image, so that's like 24 bit, 48 bit, 96 bit respectively. That is because one term describes the number of bits per channel, while the other describes the number of bits per pixel. 32 bit often refers to 24 bit, though 32 bit is actually 8 bits per channel, with an extra "alpha" channel (for transparency).
Notes: I based the 16 bit, which is kind of the key here, on experience in Photoshop, 16 bit might be different in other applications, and for other file formats (Like TIFF I think).
Also, I call RAW 12 bit, that is because in most cases RAW image files contain 12 bits of information per channel. RAW differs between camera manufacturers and camera models, so they work in very different ways. Some RAW files are 10 bit, or 14 bit. No "ordinary" camera can output more than 14 bits though.