Many superheroes are created specifically by genetic alterations. Entire teams are created usually by governments, research facilities, or wealthy individuals. Genetic alterations can take place as complete alterations of physicality or mentality. They can be discrete or completely alter someone's perceptions of reality and/or appearance. Genetic alterations for the greater good are few and far in between. More often than not those who perform and take part in genetic alterations are evil.
On the most basic level genetic alteration is a complete overhaul of a person's DNA structure. The Fantastic Four and Spider-Man are good examples of DNA alteration (pure genetic alteration) as, for the most part, their changes were less openly visible and yet still altered their genetic makeup. Genetic alterations always involve altering DNA in some way. The addition or grafting on of extraneous limbs or extremities (wings, tails, etc) are not genetic alterations. Only if these features come from a DNA alteration are they considered an alteration of genetics.
Mutants are not considered the same as genetically altered beings
Genetic alterations are more often accredited to science, though some are caused through freak acts of nature. Mutations, on the other hand, are caused through the slow process of evolution. Genetic alterations may cause mutations, but mutants are not caused by genetic alterations. Most superheroes were not genetically altered to gain their powers though, with freak accidents being a far more common occurrence.
Radiation was traditionally a popular method of altering a character's genetic/DNA composition. It has fallen out of favor in recent times in favor of more plausible methods, such as direct genetic engineering by scientists. This is mainly due to the actual effects of radiation being more widely understood than before, and now tends to be openly mocked as a method for imbuing superpowers, such as on TV shows like Family Guy or The Simpsons.