Comparisons of the four listening methods:

Browser — Talks play through your browser.
    a. Play starts after audio file is loaded – some browsers
    b. Play starts immediately – some browsers
    c. Saved to your computer – No

Online mp3 Player — Talks play through the mp3 player.
    a. Play starts immediately
    b. Saved to your computer – No
    c. Most reliable method – compatible with 98% of internet viewers.

Podcast (iTunes) — Talks play through the iTunes program.
    a. Play starts after audio file is fully downloaded to your computer.
    b. Saved to your computer – Yes
    c. Audio downloadable to iPods
    d. Automatic subscription by clicking iTunes icons.
    e. Burn audio onto CDs – Yes
    f. Download iTunes for free at:
       http://www.apple.com/itunes/download
    g. Not compatible with Windows 98.

Podcast Applications — Talks play through the podcast program.
    a. Play starts after audio file is fully downloaded to your computer.
    b. Saved to your computer – Yes
    c. Audio downloadable to iPods – No
    d. Automatic subscription – No. URL has to be entered manually.
    e. Burn audio onto CDs – Some programs can burn directly.                   CD burner software required with other podcast programs.

Definitions:

Podcast — Podcasting, a combination of Apple's "iPod" and "broadcasting," is a method of publishing files to the Internet, allowing users to subscribe to a feed and receive new files automatically by subscription, usually at no cost. It first became popular in late 2004, used largely for audio files.
en.wikipedia.org/wiki/Podcast

MP3 — MP3 is a popular digital audio encoding and lossy compression format. It was designed to greatly reduce the amount of data (10:1 compression is common) required to represent audio, yet still sound like a faithful reproduction of the original uncompressed audio to most listeners. In popular usage, MP3 also refers to files of sound or music recordings stored in the MP3 format on computers.
en.wikipedia.org/wiki/MP3