Magical Portals

The Wizard Circles are part of Wizard and Beast's henshin powers, Wizard's Connect Ring, and when a Phantom is defeated. Though all of them are different colors and have other differences that can be noticed when a viewer pays close attention. It's also part of the season logo.

Wizard
Appears when Kamen Rider Wizard casts a spell. In Wizard's Circles, gems in the similar cut his Style Rings are placed in the cardinal directions.

Red
Appears when Wizard enter Flame Style or Flame Dragon. It is the main one used by Wizard and it matches that of the Flame Wizard Ring. Also appears when Wizard powers up the Red Garuda PlaMonster.

Blue
Appears when Wizard enter Water Style or Water Dragon. It matches that of the Water Wizard Ring. Also appears when Wizard powers up the Blue Unicorn PlaMonster.

Dark Green
Appears when Wizard enters Hurricane Style or Hurricane Dragon. It matches that of the Hurricane Wizard Ring.

Yellow
Appears when Wizard enters Land Style or Land Dragon. It matches that of the Land Wizard Ring. Also appears when Wizard powers up the Yellow Kraken PlaMonster.

Beast
Appears when Kamen Rider Beast casts a spell. Unlike Wizard, who's Style Rings are put in the cardinal directions, Beast's Circles feature the animals that make up his Mantles.

Gold
Appears when Beast enters Lion Style. It is the main one used by Beast and it matches that of the Beast Ring.

Orange
Appears when Beast equips the Falco Mant. It matches that of the Falco Ring.

Green
Appears when Beast equips the Chameleo Mant. It matches that of the Chameleo Ring. Also appears when Beast powers up the Green Griffin PlaMonster.

Crimson
Appears when Beast equips the Buffa Mant. It matches that of the Buffa Ring.

Dark Blue
Appears when Beast equips the Dolphi Style. It matches that of the Dolphi Ring.

Light Gold
Appears when The White Wizard casts a spell. It is a lighter shade of Gold then the one used by Beast. Unlike Beast or Wizard's circles, who's motifs are in the cardinal directions, the White Wizard's Wizard Circle's four points shows four phases of the moon.

Translation
The circles also have a strange runic writing that can be translated.

Wizard
Outer Circle: Emerged from the magical stones, representing the great power in this world.

Inner Circle: Please release the power of devilish hidden in ring.

(devilish means demonic which could also mean Phantom (WizarDragon))

Top Circle: Please set the power of fire free.

Right Circle: Please set the power of water free.

Bottom Circle: Please set the power of earth free.

Left Circle: Please set the power of air free.

Beast
I order to all the spirits. Release the large power based on the contract with me. Great power, Land, Sea, Sky, Natural, Fourfield chief, My kin.

Trivia

 * Aside from color and center differences, Haruto and Kosuke's Wizard Circles have one other difference. Haruto's Wizard Circles are circle and Kyosuke's are more like a octagon.
 * The Wizard Circles are similar to the ones magic users have in manga and anime such as Fairy Tail, as every spell that a character uses always shows a magic circle.
 * Where Wizard Circles come out is unpredictable. Since, both Wizard and Beast can change where Wizard Circles come out, as is always use as shield from enemies attacks.
 * If Haruto uses one of Kyosuke's Rings the Wizard emblem will appear in the center instead of a Beast emblem, and it'll be a darker shade then normal. (Kyosuke's dark-blue appeard to be more of a violet when used by Haruto)