The following dinosaurs are altered dinosaurs: Alpha Acrocanthosaurus, Black Tyrannosaurus, Gigas, Armatus, and Maximus. Saurophaganax was altered to withstand using Fire Scorcher, and the Velociraptor dinosaur card was merged into a tri-move.
Gigas, Armatus, and Maximus belong to the Spectral Space Pirates. Alpha Acrocanthosaurus, Velociraptor, and Saurophaganax belong to the Alpha Gang (the last two to Seth), and Black Tyrannosaurus was created by Seth of his own accord.
There are also altered forms of the six main dinosaurs, which only appear in the arcade and DS Game.
There are several main categories of altered dinosaurs: Super, Alpha, and Black. (Though altered, Gigas, Armatus, and Maximus don't fit into any of these categories. They were altered specifically to handle the Space Pirates' upgraded Spectral Armor.)
Super Dinosaurs only appear in the arcade and DS games (called "Awakened" in the DS). There are a standard 6 Super Dinosaurs per Element, with the main dinosaurs' Super forms (differing from their species' forms in stats alone) making the count 7 each, and with Super Eocarcharia and Super Therizinosaurus being 'exceptions'.
With the exception of Super Eocarcharia, Super Dinosaurs are all colored after their Element in patterns unique to each dinosaur: Super Lightning Dinosaurs are yellow and grayish black; Super Wind Dinosaurs are light blue and grayish black; Super Grass Dinosaurs are dark and light green, and have a yellow strip down their backs; Super Fire Dinosaurs are orange, yellow, and grayish black; Super Water Dinosaurs are blue, light blue, and white; Super Earth Dinosaurs are dark and light purple; and the only Super Secret Dinosaur, Super Therizinosaurus, is ringed with black "Charlie Brown-style" zig-zags separated by a light rainbow-like gradient. There is no noticeable size difference between Super Dinosaurs and their unaltered forms.
Arcade Super Dinosaurs are "upgraded" forms of regular dinosaurs, with double the Technique and the Attack stats for each sign. At the beginning of a battle, Super-capable dinosaurs show a colored ring in the Super Dinosaur symbol which quickly disappears. If you press all 3 move buttons at once while the ring is still visible, the dinosaur becomes its Super form. However, it only stays like that for one Rock-Paper-Scissors matchup (not counting any ties). Immediately after an attack is made, the Super Dinosaur reverts to its regular form and loses half the energy it had whether it won or not.
Alpha Dinosaurs are in the arcade and DS games, the TCG, and one, Alpha Acrocanthosaurus, appears in the anime. There are 4 Alpha Dinosaurs per Element, with two from the arcade game and two being TCG-only. Fire breaks the pattern with three arcade forms and only one TCG-only. There are no Alpha Secret Dinosaurs known at this time. The term "Super Alpha Dinosaur" (arcade only) seems to apply to the dinosaurs that had a Strength level of 1400 in their original forms (Allosaurus: 1400 -> Super Alpha Allosaurus: 1800); there is therefore usually 1 regular Alpha and 1 Super Alpha Dinosaur per Element in the arcade.
Alpha Dinosaurs in the arcade and DS are all colored various shades of gray, yellow, pink, and/or dark purple. The TCG-only Alpha Dinosaurs tend to follow a different pattern, being a combination of any shade of purple, pink, red, and/or yellow. Regardless, all are controlled by the Alpha Gang, which is where they take their name from. Acrocanthosaurus's Alpha Form is commented by Ed to be slightly bigger than it's unaltered form, and it can also breath fire without a Move Card. It is unconfirmed if any other Alpha Dinosaurs possess similar elemental abilities.
Alpha Dinosaurs appear in the arcade game as separate entities from their regular forms, battling all the time as Alpha Dinosaurs. They are also distinct cards in the TCG, but the anime's Alpha Acrocanthosaurus was altered from the original Acrocanthosaurus.
Black Dinosaurs are far less numerous, with only 6 Black Dinosaurs stretched across the arcade game, anime, and TCG. The Black T-Rex is the only Black Dinosaur to currently appear outside the TCG. They are black or gray, with sparse patches and/or veins of their elemental color or one similar to it across their bodies.
Black Dinosaurs are resurrected from fossils (presumably always by Seth), and are several times bigger than their unaltered forms. Naturally, they are some of the strongest dinosaurs of all. In the anime, the Black T-Rex is likely rivaled in size only by the largest sauropods (Apatosaurus, Supersaurus, and Seismosaurus), though it is shown as far smaller than this (but still noticably larger than a regular Tyrannosaurus) in the arcade.
Like Alpha Dinosaurs, arcade Black Dinosaurs are separate from their regular forms, battling all the time as Black Dinosaurs.