What the different between a 1080I and a 1080P?

They are both the same resolution of 1920 x 1080 pixels. The "i" and "p" refer to "interlaced" and "progressive".

An interlaced signal generates a full picture in two passes of the screen. The first pass, or field, is made up of all the odd numbered lines: 1, 3, 5, ... 1079. The next field adds all the even numbered lines from 2 to 1080. Although the field rate is 50 or 60 fields every second, the full image is refreshed 25 or 30 times each second.

A progressive signal generates the full image in a single field drawing consecutive lines 1,2,3 ... 1079,1080. So, a field rate of 50 or 60 fields per second also means a frame rate of 50 or 60 frames each second.

The difference between them is that fast movement tends to be handled better with a progressive scan compared to interlaced. It also uses twice the data rate as it draws double the number of lines in any given period compared to interlaced.

Currently, broadcast signals are almost exclusively 1080i with 1080p limited to local sources such as HD games consoles and Bluray.

The field rates of 50Hz or 60Hz vary depending on the region. Europe and some other parts of the world use 50Hz while North America, Japan and some other regions use 60Hz. The difference is the result of many years of history and there is no sign of the two frame rates being merged into one rate in the near future.