Vitiligo is an auto immune condition in which the skin progressively loses its pigmentation. The result is spreading, irregularly shaped areas of skin that are completely lacking any pigment (they appear very white). There is no association between damage to the skin (such as a scratch or cut) and the development of vitiligo.
What you describe, of having areas of whitish skin develop after damage to the skin sounds a lot more like a phenomenon known as post inflammatory hypopigmentation. Essentially what happens with post inflammatory hypopigmentation is that, as part of the skin's normal healing process, some of the skin pigmentation is lost. The pigmentation does tend to gradually return, although this may often take weeks to months and, occasionally, it may never return.
I would suggest that you talk to your doctors
">primary care doctor or a dermatologist
. In addition, obviously, to avoiding cuts or scratches to the skin when ever possible (to prevent these patches from developing in the first place), your doctors may also be able to recommend some topical medications that can be used to smooth out the differences in pigmentation and improve the appearance of the patches.