You're forgetting the fact that Sonic can also transform into Super Sonic and (As of the instance of 1 game only) Hyper Sonic.
While they may not be the only Transformations featured in this video (i.e. Tails and Knuckles are the other ones I'm talking about btw.) they are in these.
Basically in the older games (Minus Sonic 1), upon defeating all seven special stages and collecting the seven Chaos Emeralds within them, Sonic gains the ability to transform into Super Sonic by collecting 50+ rings and jumping(Sonic 2 style) or double jumping (Sonic 3 style). Sonic becomes invincible, looks like a Super Saiyan, and runs faster than normal Sonic.
He can still be crushed, fall into bottomless pits, and drown in his Super form though. In addition to those draw backs, Super form also causes the player's ring count to deplete. (one ring is lost every 60 frames. Genesis runs at 60 FPS so figure it out.) Once the ring count depletes to zero, Super Sonic will revert back to normal Sonic. In newer games, Super Sonic is only used for the final battles and if Sonic's ring count hits zero in the final battle he instantly dies.
Hyper Sonic only appeared in one Sonic game: That game is the full version of Sonic the Hedgehog 3 which is created by using the Sonic and Knuckles Lock-on Technology and locking Sonic 3 onto Sonic & Knuckles. This game is called "Sonic 3 & Knuckles" this was how Sonic 3 was originally intended to be before cartridge costs made the creators split the game into two halves.
Instead of just seven normal Chaos Emeralds to collect in Sonic 3 and Knuckles there are actually seven Super Emeralds to collect as well. Sonic will lose the Chaos Emeralds and also his ability to turn into Super Sonic, because the Chaos Emeralds were turned into stone emeralds and you must play through seven even more difficult special stages and activate all seven Super Emeralds.
Upon Collecting all seven, The player will be awarded a Hyper transformation if Sonic or Knuckles or a Super Transformation with extra powers if Tails.
Hyper Sonic sparkles and flashes in about five different colors, leaves after images when he moves, runs at even faster speeds than Super Sonic can, is invincible, can create an intense flash that destroys all on screen enemies by double jumping, and can breath under water. Hyper Sonic is still vulnerable to falling off cliffs into bottomless pits, and being crushed by certain objects.
Those are the transformations.