Firstly, to answer your question, there are no similarities between apoptosis and necrosis. They are two different processes occurring due to different reasons.
Apoptosis by definition is programmed cell death. The development of an organism is regulated not only be controlling the rate of cell division but also by controlling the rate of cell death. Uncontrolled cell proliferation can lead to cancer. Hence, when cells are no longer required in the system, they commit suicide by activating intracellular signalling which leads to certain characteristic changes in the cell resulting in cell death. This process is therefore called programmed cell death. Apoptosis is a naturally occurring, programmed and targeted cause of cell death.
Necrosis, on the other hand, is a type of cell injury, that leads to premature cell death in living tissue. It can be caused due to external factors such as infection, trauma, or presence of toxins, etc., which leads to loss of cell membrane integrity and unregulated digestion of components of the cell, ultimately leading to cell death. Necrosis doesn't follow the signalling pathway as apoptosis, instead,involves activation of certain receptors which lead to cell death.
Relationship of apoptosis to development and repair can be answered by certain examples.
For instance, in the developing limb of human embryo, the webbing between the digits is removed by apoptosis, without affecting the cells of the digits.
Another example is rat liver, the most studied model of tissue regeneration. In this case, if a part of a liver is removed in an adult rat, liver cell proliferation increases to make up the cell loss. If the same rat liver is chemically induced causing its enlargement, the process of apoptosis is initiated and increases until the liver returns back to its original size.
Is one similarity- cell death in both pathways is induced by this same factors, for example toxins. The dose of toxin is a key, which way of death will be chosen by cell. Low dose of toxin- apoptosis, high dose - necrosis. Mitochondrial membrane permabilization in apoptosis is selective for outer membrane, in necrosis concern both membranes.
Generally speaking all these previous answers are correct and both the mechanistic and phenotypes shown by apoptosis and necrosis are very different, unless you go into very specific cell models or very specific pathways. Necrosis can be mediated by caspases, similarly to apoptosis, in macrophages that activate an inflammatory response, therefore if you just look at caspase 3 activation and not at caspase 1 activation you could confuse the necrotic response for apoptosis...HEK cells, on the contrary, apparently don't have a functional caspase 3, and execute caspase-independent apoptosis, therefore if you were to simply rely on a caspase 3 test to evaluate apoptosis vs necrosis you would be misguided.