You will undoubtebly get different anwers and i am no expurt, but bh to me is finding loopholes and exploiting them even if they are against the tos for whatever agent you are using, wh is just doing things conventional by-the-book and as listed by the stated tos... gray hat would be inbetween obviously, but where you exploit system loopholes but they do not violate the terms of service... this is just my opinion and i am sure others will chime in with their own.
per your example using backlings to affect g**gle serps:
bh = link farms, etc. where this type of linking breaks g**gles tos
gh = using a forum profile signup bot for a link on member spages
wh = finding blogs relvant to your kw and posting comments relevant to the op blog post