There are three main styles of TKD: traditional ITF, modern ITF, and Olympic WTF. The traditional ITF and modern ITF styles use the Changhon pattern set (which includes Toy-gye), while the WTF uses a different pattern set. There are other TKD pattern sets but the ITF and WTF ones are the most prevalent.
As to your question about Toi-gye:
- Scooping block. A deflecting block is where the blocking palm move in a “U” shape motion, downward and then upward, under the attacking arm or leg, lifting it up until the attacking fist moves over your head or the attacking leg moves so high it unbalances the attacker.
- Circular block. A deflecting block is where the blocking arm moves in a circular path and pushes the attacking arm or leg to the side so the attack misses your body.
- Traditional ITF circular block method. Gen. Choi , in his 1965 first edition book Taekwon-do, The Art of Self-Defense, states that the Toi-gye movement as using a middle section circular block, which he describes as an inner forearm block that first moves in a circular path and ends with fist at shoulder height. There is no springing of the knees, only a snap of the hips.