Well and even that has to be explained a bit.

Normally, when we talk about 720p we mean 720p at 60 frames per second. 1080i normally means 1080i at 30 frames (60 fields or half frames) per second and 1080p typically means 1080p at 60 frames per second.

However, there are other types that could theoretically be sent over component, such as 1080p at 24 or 30 frames per second. Component should have enough bandwidth for both of those.

When we talk about broadcast TV it should also be mentioned that 1080p does not exist as a broadcast standard. 1080p only is possible when using computer equipment, HD-DVD, Blu-Ray or other equipment capable of passing the signal.

To repeat that, 1080p cannot currently be handled by any HD-TV medium, whether it be satellite, cable, etc. at least as far as I know. It is not really part of the HD-TV spec.