iPod is an Apple product that allows you to play MP3 and other (usually compressed) music files. Although Apple did not originate the product -- the Diamond Rio was the first popular model -- Ipod is by far the brand leader in the market for MP3 players.
An MP3 player is any product that allows you to play MP3 and other music files.
The major difference from a practical viewpoint is that though, for example, the iPod Nano model, is a great little player -- good screen, decent sound and decent headphones (whatever some say) unlike most MP3 players it is requires proprietary software to be installed on your computer in order to load music files onto the player.
This is, in itself, an unnecessary nuisance -- most non-Apple MP3 players simply appear on the computer as an extra disk drive and allow you to drag music files from the computer and drop them into the player.
Unfortunately, the iTunes program which Apple forces you to use is not the best for the purpose -- many people find it frustratingly opaque and overly complex.
Another objection is that the iPod is designed to prevent one sharing files and the can only be connected to a single computer (2 if you have both PC and Mac) which can lead to problems if the computer or the iPod crashes.
If you are interested in comparing the iPod with other players I would suggest looking at reviews of products from Sony, Sandisk/Sansa, Creative, iRiver, Cowon, Samsung.
There are also many cheaper MP3 players of lesser brands or from unknown brands which will do the job -- but, usually, they have small screens or are awkward to use in other ways.
Can anyone give me the definition of an ipod and an mp3 player and tell me the difference between them? Thank you. user470

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