What is the difference between "offline editing" and "proxy"？

In a full "offline/online" process, a staple of editing since we've had digital media, you replace the full-quality media with the proxies you created separately for the editing process. Then when done, replace the low-res proxy media with the original media at the end of the editing prior to exporting.

In Premiere's "new" process, you import the original media, select it, tell Premiere to "create proxies", and when Me is done creating them, they are shown in the Project panel separately from the original media. In a sequence, you can switch immediately from original to proxy and back to original as you wish. So ... you can do playback with proxies enabled for better playback, switch to original to see the quality of the effects, and back to proxy for playback.

Each has strengths and limitations. A couple issues for the new Premiere proxy process are time-remapping and matching total/type of audio channels. Other than those, it's pretty slick.

Neil

The answer is in the links you posted.