You're right in that i and p mean interlaced and progressive. The i/p simply means it can do both 1080i and 1080p. There are no interlaced 720 formats.
'Native' mode means only the captured frames are recorded, no pulldown is added. Otherwise, pulldown is added and the 24p original is 'embeded' into another format, usually 1080i/30.
There are so many cameras, capable of so many different formats that providing a manufacturer and model could be helpful in this discussion.
Jim's answer is absolutely correct but I'm going to re-state for clarification.
The i/p designation means you can chose to record as interlaced or progressive for a given resolution.
It sounds like your camera is designed to "capture" images at 60 frames per second, selecting "native" mode means extra frames are deleted and only the desired frames, based on frame rate setting, are recorded to memory. The advantage of "native" @ 24fps is you save space on your memory card. The advantage of NOT using "native" mode is that all 60 frames per second are recorded, but the file metedata tells playback software to only show the frames needed for the specified frame rate (i.e. 24). Since all 60 frames per second are recorded, you use more memory but you also have the option of retrieving all the those frames, if you so desire, at a later time (i.e. for smoother slo-mo).
To be honest I don't know what your spec of 1080i/24p means. If that is truly an option then I would guess it means it will record a 24p image but the metedata would indicate the file should playback at 30fps interlaced by adding the proper 3:2 pulldown. This would give you that "film" look in a broadcast compatible format.
For the most part, you don't want use use any interlaced settings. Very few display devices still in use can properly display interlaced images. Interlacing is only required in some broadcast specifications.
To answer the second part of your question;
Frame rates are an indication of how many times the moving image is captured over a given period (per second). Higher frame rates means smoother, more "real life" motion. Data rates can generally be considered an indication of image or audio quality. Higher levels of compression result in lower data rates and (generally) lower quality. If squeezing more hours of footage on fewer memory cards is more important than getting the best image quality, choose a lower data rate. Higher frame rates (more images per second) inherently require a higher data rate to retain the same quality as fewer frames at a lower data rate.
It sounds like your camera is designed to "capture" images at 60 frames per second, selecting "native" mode means extra frames are deleted
That's highly unlikely to be true, at least for 24p. It's almost certainly the other way around. In 24p mode, the camera 'captures' 24 frames and than adds the necessary pulldown to turn that 24p into 30i.
So, in that case what's the significance of the i vs the p? It's really the settings like 1080i/24p that are confusing me. How can video be both interlaced and progressive? Naturally, I assumed the letters must mean something different when talking about data rate or shutter speed, as opposed to resolution.
If it helps, the camera is a Panasonic AP-HPX 250 and I'm looking to record in AVC-Intra 100. We output for YouTube and for video DVDs, so I'm trying to figure out the ideal source video formats to shoot for each. Sorry to ignore the thread for so long. Work took over.
Providing a camera model is very helpful in answering your questions.
Indeed, the 1080i/24p setting on that camera will "capture" a 24p image, add a 3:2 pulldown and record it at 30i.
This particular setting is to obtain a 24 fps "film look" in a file prepared to be edited with other 30 fps footage for broadcast distribution.
If your primary destination is computer display, you should only use progressive recording formats. You should select your progressive frame rate based on the motion "feel" you're trying to achieve and/or to match the frame rate of other footage it will be combined with.
It's really the settings like 1080i/24p that are confusing me.
Understandably, as there is no such standard, and the nomenclature is incorrect.
The proper method is to list the horizontal resolution, an i or p, a slash and then the frame rate (never list field rate), as in 1080p/24.
The shorthand is to drop the resolution and the slash, and move the i or p after the frame rate, as is 24p.
Camera makers get this wrong ALL the time, which leads to a great deal of confusion.
Shoot 1080/24PN and you should be fine.