The BBC introduced high-definition television in 1936, with 405 total scanning lines (well, it was HDTV by the standards of the time). Modern HD started in the 1980s with a Japanese analog standard, 1125/59.94, with 1035 active scanlines, interlaced. Europe also developed an interlaced analog system, called Eureka, using 1250 scanlines total and running at 50 fields per second. Both systems used the 16x9 widescreen aspect ratio.
Both systems have been made obsolete by digital HD standards, and any program content you encounter from the earlier systems will have to be (and probably already has been) converted to one of the current standards, since analog HD capture cards for the Mac are nonexistent.
Digital HD falls into two camps: 1080-line standards and 720-line standards. The 1080-line standards evolved from the earlier 1035-line standards and run at 25, 29.97, and 30 frames per second interlaced, and 23.98, 24, and 25 frames per second progressive (although the recording is interlaced, the image capture is true progressive).
PsF (progressive segmented frame) recording of 1080p24 HD
You'll see the terminology 1080i for the interlaced formats, and 1080p for the progressives. FCP tags the HD formats with their image-update rate without respect to fields or frames: 1080i60 is 30 frames per second, interlaced (thus 60 fields per second); 1080p30 is 30 frames per second, progressive, no separate fields.
The 720-line formats, all progressive scan, started as a lower-bandwidth alternative to 1080i with roughly the same vertical resolution (no Kell factor degradation to account for). 720p normally runs at 60 frames per second, but there is a 30 fps variant, and 24 fps images are recorded on DVCPROHD equipment by performing a 3:2 pulldown, repeating each 24 fps frame either twice or three times in alternation to fill up all 60 frames on tape. 720p DVCPROHD even allows arbitrary frame rates between 1 and 60 fps to be shot; it flags each "new" frame with a special code to set it off from previous repeat frames in whatever pulldown sequence is required.
DVCPROHD recording of 720p24 as 720p60
As in the 1080-line formats, 720p can run at either integer frame rates or the NTSC-compatible rates 23.98, 29.97, and 59.94.
High-definition formats include the "integer NTSC" rates, especially 24 fps, for direct compatibility with film production. Film is normally produced for release at 24 frames per second, and having a true 24p mode, along with 30p and 60i, lets HD transfer to film with the exact same timebase. Filmstyle production often uses separate audio recording ("double system" audio), and having the exact same timing for film-originated and HD-originated material simplifies postproduction considerably.
However, the NTSC-derived television world still uses the fractional rates 23.98, 29.97, and 59.94, so that HD and SD material can share a common timebase (and so HD material can be played out using existing NTSC-oriented scheduling and automation systems). Film transferred to television in NTSC countries is slowed down one part in a thousand to match the fractional rates. (That's not so bad, really: in PAL countries it's sped up 4 percent to 25 fps.)
Almost all HD material is shot at PAL rates or fractional NTSC rates. Integer NTSC frame rates are sometimes used when HD material is to be used in a movie shot (and finished) on film but are rarely seen otherwise. Regardless, HD material is usually described by integer rates, so a 1080i60 clip may be shot at either 59.94 Hz or 60 Hz, and a 720p24 clip might be either 23.98 fps or 24 fps.
Final Cut Pro handles only NTSC-compatible and PAL-compatible frame rates for DVCPROHD over FireWire. True 24, 30, and 60 fps material can't be ingested using FireWire, though third-party uncompressed cards may allow it.
Sampling and Pixels
The HD formats themselves are specified using square pixels. A 1080-line HD image has 1920 pixels per scanline. A 720-line image has 1280 pixels per scanline.
"Full bandwidth" HD recording formats record all those luma samples, but normally subsample the CR and CB color-difference signals with the 4:2:2 ratio described earlier. (HDCAM-SR allows recording the original RGB signals in their full-resolution 4:4:4 glory: no color-space conversion, no subsampling. It's popular with the high-end film effects crowd.)
"Camcorder" HD formats usually subsample the luma signal as well as the chroma in order to get the data rate low enough to record on tape. As with subsampled chroma, the subsampled luma is interpolated back up to full resolution for conveyance over a serial digital interface.
"High Definition Fundamentals" in "New Features in Final Cut Pro HD" has a lot of great information on HD formats, terminology, and the like. Get to it from inside FCP HD (4.5) by choosing Help > New Features. (FPC 5's documentation does not contain this information.)