What is the difference between 1080p and 1080i on a HDTV?

It's to do with the resolution. The 1080 identifies the number of lines that create the image, so 1080p and 1080i have the same number of lines. The letter stands for the type scan the TV uses. The P stands for progressive and the I stands for interlaced. Progressive will process the image twice as fast as interlaced and therefore produces better colour and clarity.