In very broad strokes, that is correct (though this doesn't do justice to the mechanisms - mutation, natural selection, genetic drift, epigenetic influences, etc.) by which this occurs.
But it is essential to bear in mind that the evolutionary process is extremely slow - so slow as to be virtually undetectable on a generational level. Thus, at no time is it expected or necessary (in the case of sexually reproducing creatures) for an individual to mate with another individual whose genome exhibits a marked difference.
I commend you on your open-mindedness, and would encourage you to consult someone in your circle of friends and acquaintances with a background in Biology who can better explain this to you.
Regards,
You both might like to read this book: http://www.amazon.com/The-Science-God-Convergence-Scientific/dp/1439129584
It makes some interesting and well supported claims. I enjoyed the read and reread it as it was packed dense with information.
Here’s a video if you don’t like to read:
https://www.youtube.com/watch?v=EhrdtTG0nTw