What's the difference between killstreak, specialized killstreak, and professional killstreak weapons?

Solution 1:

This is taken directly from the wiki:

Standard

...simply add[s] a HUD kill counter

Specialized

...adds a kill counter as well as a colored sheen that intensifies as streaks increase

Professional

...in addition to adding a kill counter and colored sheen, also causes the weapon to add a particle effect to the user's eyes (similar to the Eyelander) that intensifies with kills

Source: 1 | 2