Correct. Specializations are a dice pool bonus, not a skill increase. Only a few things actually increase skills - adept improved ability, reflex recorders, and move-by-wire (the latter increases your dodge skill).
Because SR4 uses skill + Attribute, increasing your Attribute also increases your dice pool - things like muscle toner and cerebral boosters are much more important in SR4.
And finally, there are lots and lots of adept powers, gear, and augmentations that simply give a bonus to different dice pools. A rating: 6 medkit gives you 6 bonus dice for first aid. Synthcardium: 3 gives you a +3 bonus to athletics tests. Kinesics: 3 gives you a +3 bonus to social skill tests. And so on.
Dice pools are variable in SR4. For some things, having a dice pool of 12 means you are very, very good. For other things, having a dice pool of 12 is still very, very good, but someone who is mediocre can have a similar dice pool simply by having a few relatively common dice pool modifiers - and someone who is very, very good and who also uses those helpful items will be superhuman.