There are varieties of Tae Kwon Do, not all Tae Kwon do styles are same there are slight difference between WTF(World Tae Kwon Do Federation) ITF(International Tae Kwon Do Federation) and Pro Tae Kwon Do.
Most popular version would be the WTF Tae Kwon Do which is now playing in Olympic. The Taekwondo institute in Ameica is also mostly WTF style. Some of them are known as ATA (American Teakwondo Association) but still shares most of style with WTF.
However what North Korea mostly likely to do is ITF style of Taekwondo. ITF style was created by Korean-Japanese people in Japan which allows more aggressive attacks using knees and more variety of hand use. Since N.Korea had contnuous interaction with Japan that N.Korea brought most of Taekwondo martial artist from Japan that becomes the standard style of N.Korea's Taekwondo.
Since its allowance of using knee and hand technique consider more brutal and powerful than WTF style. WTF Style is more suitable for sports and standarization for Olympics.
South Korea and North Korea, both teaches Taekwondo as necessary military martial arts. The military version of South Korean Taekwondo is almost aggressive as ITF style. There is also Pro TaeKwondo which is somewhat similar to ITF version of Taekwondo that allow to use knees and direct punch attacks on the head. Also the uniform (도복, Do Bok)shapes are different. ITF Taekwondo wears uniform with some stripe lines on the side where as WTF wears mostly plain white color uniform
WTF Taekwondo has standard rule in Olympics and still changing rules in order to achieve more dynamics of game.
1. No direct attack on head by hand
2. Fancy kick counts more points (New Rule)
3. Stron Punch below sholder only counts as a point
4. No attack on the person on the ground
5. No attack on the behind
Also they add new gears that counts points automatically which will show in 2008 Olymoic.
Here's video clips compare the difference.
North Korean TKD (Taekwondo) Demo team
South Korea's WTF TKD
Besides TaeKwonDo there variety of Martial Arts that are originated in Korea.
There are so many Korean Martial Arts
This is South Korean military Martial Arts besides TKD known as Teokong MuSul
Korean Traditional Martial Arts similar to TKD, Taekkyun
It has combination of kick in the distance and grappling in close range
This Takkyun's basic movement looks like a dancing but it is the key element of Taekkyun. The flexibility reveals the most when the person is relaxed without any tension therefore they continously move with flexible gestures. The strong stick can be break easy but flexible things never breaks but bend. This is the key terminology behind the Taekkyun.
Korean Wrestling, SSIREUM, similar to Mongolian Wrestling
Most recently invented South Korean Martial Arts Gong Kwon Yu Sul, created in 1997
It is creadted by a guy who have done various martial arts and combine the best of each martial arts and becomes the Gong Kwon Yu Sul. Most of moves are combination of Mixed Martial Arts(MMA) resemble to UFC or Pride.