Question about Twin Terrors

On the skill tree it says it increases "weapon critical hit chance", does that mean it actually modifies the critical hit chance you see on the weapon? e.g. having a weapon with 10% crit chance, taking the cluster that gives a total of 125% increased weapon crit chance, gives your weapon 22.5% crit chance when dual wielding, at which point is then multiplied by your regular "increased critical hit chance"?

Or is "weapon critical hit chance" the same as "increased critical hit chance", but it was only worded differently in this case for some reason?

First of all its "increased critical strike chance" (ICSC).

Second, ICSC applies to everything, spells and Attacks.

Increased WEAPON critical strike chance (IWCSC)only applies to Weapon damage, therefore only for Attacks and Attack Skills, not for spells!
Split Shot is an attack or dual strike, Freezing pulse is a spell.

The critical strike chance on weapons as shown is only modified by weapon boni IMO.
But the overall critical strike chance will be shown in your character profile.

Your base critical strike chance is 5.
Any bonus applies to this value.

So if you got 300% increased critical strike chance, you are at 20% chance for a critical hit.

If your Weapon has a base 10% critical strike chance, you are at 40% chance for a crtitical hit.
IWCSC and ICSC apply to the base value of the weapon.

100% from IWCSC and 100% from ICSC would therefore be 200% combined, therefore base chance of the weapon (10% in this case) + 200% = 30%

Changing your weapon will therefore have a huge impact on your critical strike chance.

My question is more about how Twin Terrors interacts with increased critical chance.

Let's say I have a 10% crit weapon, 100% increased critical chance, and 125% increased weapon critical chance through Twin Terrors and the nodes leading up to it.

How does that work out?

Is it:
10% base critical chance * 2.25 = 22.5% base critical chance,
22.5% * 2 = 45% crit chance?

Think of it this way:

There are two different critical strike chance stats, one for Attacks, one for Spells.

Increased Critical Strike Chance increases both.

Weapon Critical Strike Chance increases just the one for attacks.

Spell Critical Strike Chance increases just for spells.

Using your example, you have 100% increased crit chance with spells, and 225% increased crit chance with attacks. As such, factoring in your base crit chance plus your weapon's 10% base crit chance, you have a 33.75% chance to crit with weapon attacks.

Oh I see. So it's additive with increased critical chance, but only applies if you attack with a weapon.