If you assume that a specific rule trumps a general rule, then we come to the following conclusions:
Specializations add 2 dice to any tests made for that skill. . .
This is a
general statement of intent, "you get two dice added to your die pool".
A specialization grants the character a dice pool modifier of +2 dice on tests using that skill when the particular specialty applies.
This is the
specific rule on how to implement the intent stated on page 121.
Therefore, if you apply "specific trumps general" logic (and if you don't, every RPG I've looked at falls apart), a specialization is a die pool
modifier.
Furthermore, to clarify what FastJack was getting into,
The Shadowrun rules often call for a plus or minus dice modifier to a test. These modifiers can result from injuries and situational factors that affect what a character is trying to do.
Note the section header,
Dice Pool Modifiers. This section defines dice pool modifiers and gives you two choices:
(a) Injury dice pool modifiers
(b) Situational dice pool modifiers.
Further along:
Unless otherwise stated, any modifier mentioned is considered to be a dice pool modifier.
So anything that is not part of the basic dice pool is a
dice pool modifier.
In fact, we've got another clear statement of intent:
When a player makes a test, she rolls a number of dice equal to her dice pool. This dice pool is the sum of the relevant skill plus its linked attribute, plus or minus any modifiers that may apply.
As previously stated, all modifiers are dice pool modifiers unless explicitly stated otherwise. Further, a dice pool consists of exactly three things,
skill,
attribute and
modifiers. Therefore, at any point, whatsoever, in which the book says "this adds dice to your dice pool", per the aforementioned quotes, it is always a dice pool modifier. Therefore, when splitting your die pool, per the RAW, you take skill + attribute, divide as you desire, then add anything else relavent to the test.
I see absolutely no other interpretation available, barring errata. Specializations and Weapon Foci (and EVERYTHING ELSE) are all dice pool modifiers, added after you split.