The difference is really all in the drivers. A Quadro uses drivers that are heavily designed to produce high-quality, accurate output; a Gaming Gpu uses drivers that are optimized to run quickly, at the cost of not producing pixel-perfect output. In gaming, the graphical difference is unnoticeable - it's only really visible in CAD applications and high-quality animation rendering. Workstation drivers also frequently optimize much more for OpenGL, while gaming cards are slightly biased towards Direct3D.
There are sometimes hardware differences. Historically, workstation cards had more memory (usually 512mb/1gb when gamer cards had 256mb/512mb). Some also support an obscure feature called an "external clock signal", which can be used to...