You got 720p,1080i and 1080p
720p is 1280 x 720 pixels in Progressive refreshrate. That means every refresh moment all the lines [even and odds] are replaced
1080i is 1920 x 1080 at interlaced refreshate. That means every refresh moment either the even or uneven lines are replaced.
1080p is 1920x 1080 at progressive refreshrate, That means every refresh moment all the lines [even and odds] are replaced
Progressive is best for action and lots of movement, because it refreshes the whole screen at one time you won 't get possible screen tearing [where some lines in the screen seem to still hold the old image.]
Interlaced was long ago developed, our old standard definition broadcasts we're all interlaced. Why? Only having to replace half the lines means less bandwidth is needed. Meaning more channels you can put on a connection.
Interlaced is fine to slow moving or non moment images but for quick moving images well.. you might get screen tearing.
So 1080p is best, then 720p [due to being progressive] and 1080i follows. It will give you full HD but interlaced isn't as good as progressive.
Now some say 1080p - 1080i - 720p, but I disagree.. progressive beats resolution!
The PS4 will run perfectly at 1080p, and also will support 1080i. Yes it also has a fallback to 720p if your television is that old. 720p still is an official HD standard.. and the PS4 will support it!
Many if not all games on the PS4 will run at 1080p or close to that naturally. The PS3 generation runs most games at 720p. Only a very few run at 1080p! The PS4 generation will allow all the games to either do 1080p or get really close to!