I am not fully clear on the meaning of your question. I am guessing it amounts to what are the major drivers of evolution.
Natural selection is the natural environment's affect upon a population's collective genome(s), molding it to be its most adaptive in that environment.
(Adaptive meaning reproducing to generate reproductive offspring.)
Besides natural selection there are similar selections under the control or influenced by people (artificial selection). Not all the effects of human selection are the result of human intent.
Some traits can arise when something else is under selection (see
fox domestication). Foxes were basically selected for tameness (being "friendly" to humans). It resulted in foxes with more juvenile traits and neurochemical changes, among other things.
Other selections can be unplanned but very useful (see
wheat domestication). It is thought that repeated cycle of ancient people harvesting and then sowing new crops of pre-wheat resulted in a selection for plants and seeds that were better suited to being a domesticated crop (larger seed, seeds stay on plant until harvested).
The biggie in my mind however is
genetic drift which works generally in opposition to various kinds of selection. Because it changes genomes, it is considered an evolutionary process. Drift causes sequences not under strong selection to maintain some function to change randomly over time.
Both drift and selection can operate at the same time. In larger populations, selection will have stronger effects. In smaller populations the effects of drift will be increased. Very small breeding populations (such as in research labs or in small breeder establishments) drift can often have inadvertent adverse effects.
Other evolutionary influences might include mutation, migration/isolation, and indirectly environmental disturbances. These could be natural, human caused or human influenced.
There are also drivers internal to the genetic system like
selfish genes and
molecular drive which can result in the amplification of particular genetic elements.