Correct, 1920 x 1080 progressive scan is the long name for 1080p.
Nothing is being broadcast in 1080p because the amount of data required for that format is prohibitive. And the upcoming blu-ray and HD-DVD formats most likely will not be in that format, either, for the same reasons.
There are some panels and some DLP chips that will do 1080p now. The 1080i broadcasts look great on those displays, because no downconversion is needed to display them. The odds of you actually seeing something get broadcast in 1080p is pretty slim at the moment.