Genetic determinism is the idea that genes determine behavior. Sometimes genetic determinists are accused of positing that all behavioral trends can be understood by genetics alone.
The blank slate is the idea that for all people (regardless of sex, race, etc.) the mind begins its development at birth (or maybe some earlier stage) from the same (or almost the same) beginning state. The metaphor is that the mind at birth is a blank slate waiting to be written on. Sometimes this group is accused of ignoring real differences between groups.
As an example genetic determinists might argue that gender roles are largely coded within our genes and that differences between adult men and women can be accounted for mainly genetically. On the other hand advocates of the blank slate might argue that men and women start out with the same minds but that the influence of peer pressure, advertising and social norms change their developmental paths so that men often end up with one set of psychological features and women another.
As another example one could argue that intelligence has a significant genetic component and that twin studies demonstrate this. On the other it might be that intelligence is determined by how people with certain physical attributes are treated.
As one measure of intelligence (IQ) has shifted significantly with time the rival camps give differing explanations: Evolution is increasing intelligence within humans in the 20th century; Schooling is of a higher quality (or more universal) than before.
As a final example consider personality disorders. One might argue that criminal behavior is genetically determined. If so tests for the relevant genes would open up significant social issues. On the other hand it might be argued that personality disorders mainly arise from mistreatment in childhood and that if only we could prevent childhood abuse or improve support for children we could all but eliminate criminality.
The main problem with the above arguments is that they all make use of the either/or fallacy. They assume that either there is a clear and simple causal link from genetics or there is a simple causal link from nurture.
Now of course there are also environmental causes (such as nutrition) for behaviors but the either/or fallacy is still a problem even if we incorporate all three types of causation.
There is an implicit assumption that the different causes do not interact or that even if they do that they can be teased apart easily.
This debate has significance in discussing free will and the 'soul' because causality is often called upon to argue that a causal physical universe cannot be all there is as then everything you do would be determined by environment, genetics and societal influences on your development.
If on the other hand there is no easy way to calculate your future behaviors from knowledge of these three categories of influence then this makes the argument dubious. It essentially depends on ignoring the horrendous computational complexity involved in actually performing such a calculation.
Lets look at other possibilities!
The factors might interact in a fairly straight forward way. E.g if you have a genetic predisposition to Alzheimers and contract the herpes simplex virus (cold sore) then you are very likely to develop Alzheimers.
The factors might interact as coupled differential equations. E.g children may genetic dispositions and may simply copy the most successful adults. Teenagers may copy each other. Through such behavior complex results may emerge (the emergence of chaotic patterns from simple rules).
Finally there may be developmental accidents. In a baby's developing brain there may be multiple ways to perform certain mental tasks. Which one the brain picks may be a matter of chance but have significant repercussions later on in terms of their behavior.