In the first, the idea is that our genes determine how long we live. We have a gene or some genes that tell our body how long it will live. If you could change that particular gene, we could live longer.
The second theory is that over time, our body and our DNA get damaged until we can no longer function properly. The idea here is that how long we last is really just a consequence of small changes in our DNA. These changes add up until the total amount of damage is too much to bear and we die.
It matters which theory is right, as it will determine how to push the limits of aging. For example, if how old we live is in our genes, then to increase our lifespan we may be able some day to change those genes. If on the other hand, our final age is based on the accumulated damage of a lifetime, then we could try to minimize that damage to live a longer life.