WIZARD'S ENERGY TWISTER SKILL MECHANICS
The Wizard's "Energy Twister" skill works differently on consoles than on PC: the PC version received a nerf in patch 2.4.2 season 7 which removed the ability to corner-stack twisters. However, this fix was never applied on consoles, and along with lack of casting animation, the Twister is the strongest skill for Wizards and Wizard in general is one of the strongest, if not the strongest, class on consoles.
DIFFERENCES VS THE PC VERSION
LACK OF CASTING ANIMATION
Casting a twister on consoles does not interrupt the channeling, allowing you to fully benefit from channeling boosts, such as Mantle of Channeling, Taeguk gem and Deathwish, further boosting the damage as opposed to PC version. Due to this animation difference, these items are often included in all twister build variants.
CORNER STACKING MECHANICS
Since patch 2.4.2 (season 7), the twisters on PC despawn when they hit a wall. For consoles, the mechanics still work as they did pre-patch, which means that it's possible to stack twisters in tight corridors and corners and let them bounce, dealing way more damage. It works in any narrow corner and is especially useful versus rift guardians, that can die sometimes so quickly that you don't even need to wear Stricken. In open maps, you can use inverted corners and aim at the wall, see this video guide.
DMO AND LOD VARIANTS
The two builds aim to boost the damage of the twisters themselves, using skill multipliers such as The Twisted Sword, Etched Sigil, Ranslor's Folly and Valthek's Rebuke. The builds are heavily centered around Area Damage, similarly to the PC version. However, since the twisters on consoles do not despawn when hitting a wall, you are not limited to using the Wicked Wind rune and in fact can choose any (i.e. Mistral Breeze can be used to proc Bane of The Trapped from a distance). That said, WW is often used to negate the effects of Valthek's Rebuke.
New since season 23, the reworked Firebird set buffs non-channeling fire skills. Since twister has a fire rune, it was not long before Firebird Twister was born on consoles. However, it is a common mistake among players to assume that the damage is done by the twister skill multipliers -- it is Firebird set bonus that does the damage, the twisters are only means to an end, a way to quickly fill the entire screen with something that constantly procs Firebird damage. Hence why twister skill multipliers (i.e. The Twisted Sword) do nothing for this build.
Ranslor's Folly are very often used for their grouping abilities, not for the twister damage.
The extra twisters spawned by Etched Sigil can be used with Ranslor's Folly for further grouping, but those extra twisters will not proc firebird damage.
Similarly to PC, area damage does not work at all for Firebird, so even though other twister variants use AD, it does not work here.
TAEGUK AND RCR INTERACTION
The Taeguk gem has a hidden mechanics, where it stops working when the channeling skill does not consume any resources. With wizards it can happen a lot, since there are 2 important skills that reduce the costs of all skills: Diamond Skin - Prism and Storm Armor - Power of The Storm. The former is a staple in Firebird Twister and the latter is a staple in DMO and LoD variants. Using one of these skills (or both), along with low attack speed and/or too much RCR (Leoric's Crown, Hergbrash's Binding, Captain Crimson's set, etc.) can put you above the Taeguk threshold.
How to know if you're above: stand in town, equip your gems and gear, turn on your Diamond Skin/Storm Armor and just channel: if you lose Taeguk stacks or can't see them at all, you need to fix it.
How to fix it: increase your attack speed or reduce your RCR.