TV resolution/compatibility My TV is a Sanyo HDTV, 1080p. I heard that if shoot at 720p the quality of the video is the same. 

Can anyone explain if there is a difference between the two resolutions, and in which case I use one or the other?
Whoever told you that was wrong.  "1080p" has 1920 horizontal pixels and 1080 vertical pixels.  "720p" has 1280 horizontal pixels and 720 vertical ones.  See this wikipedia page.  You would want to use 1080p whenever you want the highest quality your television is capable of reproducing.  The only reason you'd use 720p is if file size is a concern, or if your television doesn't really go up to 1080p.