The "i" and "p" in video formats stand for "interlaced" and "progressive" scan, respectively. The resolution is the same, which is why the number is the same; the difference between the two is in how the image is displayed.
When it's time to display an image, a TV or computer monitor will draw each frame line by line, starting from the top, until a complete image has been drawn and then it starts over, drawing as many complete images as the frame rate dictates (24, 25, 30, 50, 60 depending on the source). Even at 25 times a second, it's fast enough that you don't notice and it gives good picture quality. That's Progressive scan.
Interlaced scan, on the other hand, starts out the same way. It draws the first line at the top of the display, but then it skips every even numbered line until half of an image has been drawn. When it starts over, it starts at the second line and proceeds to skip all the odd numbered lines that have already been drawn until the other half of the previous image has been drawn. It does this faster than progressive scan (50 times in PAL [http://upload.wikimedia.org/wikipedia/commons/thumb/0/0d/PAL-NTSC-SECAM.svg/1000px-PAL-NTSC-SECAM.svg.png] regions, 60 in NTSC [http://upload.wikimedia.org/wikipedia/commons/thumb/0/0d/PAL-NTSC-SECAM.svg/1000px-PAL-NTSC-SECAM.svg.png]), but only ever draws half images at any given time.
When it's done right, Interlaced video is fine, but it's really a (dying) Television standard from the days of CRTs. LCD or Plasma displays never (as far as I know) work in interlaced mode. So when they get an interlaced video signal, such as a TV channel or your Xbox in 1080i mode, it has to do something called deinterlacing [http://en.wikipedia.org/wiki/Deinterlacing] before showing it to you. I'm sure you've seen bad or absent deinterlacing before... it looks like this:
More reading [http://en.wikipedia.org/wiki/Interlaced_video].