Let me try to explain in laymans term...
Dont be confused with video signal (1080p, 1080i, 720p, etc) to screen native resolution (1366 x 768, 1920 x 1080, etc).
Some 720p LCD panel (native resolution is 1366 x 768) can accept video signal of 1080p but it is not a FULL HD and it scales 1080p signal in the 1366 x 768 resolution.
While 1080p LCD panel (native resolution is 1920 x 1080), can of course accept FULL HD signal and does not scales 1080p video signal.
There might not have noticeable differences in 32" panel if you are using video signal such as upscaled DVD, or any 1080i and lower resolution sources. But if you are using BD player or a 1080p sources or a PC then even at 32" you will certainly notice the differences.
Also there are many other things to consider in a display panel, the panel itself, the video engine used, other features such as the response time, native contrast, refresh rate... among others.
Note that P (progressive) shows all horizontal scan lines like in 1080P, all 1080 lines are being shown at the same time, while 1080i (Interlace) shows only the alternating scan lines at a given time (1080 / 2 = 540 scan lines; it shows 1, 3, 5, 7, 9 ...... 1079 scan lines for example). Some panel or even source player can compensate missing lines or frames to show better scanning.