The whole 'fast' and 'slow' thing is kind of confusing until you remember that evolutionary bilogists usually talk on time scales of millions of years. Speciation can be 'rapid' in the sense that it can take only a few thousand generations to achieve. You are STILL talking about many thousands of years for something like humans which have life spans in the decades. Bacteria can go through the same number of generations in a few years, and striking evolutionary changes have been seen in just that amount of time.
The 'random seed' for evolution is the small amount of genetic differnce you share with your parents. You are not a clone of your parents, you are a combination of the two, and yet unique in yourself. Plus, small mutations may have arisen, most of which will be completely unnoticeable. It is the addition of many such small changes that result in a changed species over many generations.
Ya'll's replies are getting longer and longer
and making less and less sense.