We can think of cells as running interactive programs.
Much work has been devoted to the role of genetic instructions codified in DNA. As part of it, much focus is in tur devoted to genetic mutations which can change DNA's encoded instructions. On the other hand, recent focus has been made on what is called epigenetics, or the structural modification of DNA structure either by chemical modifications or by interaction with other molecules which changes the way in which the genome is expressed.
During morphogenesis, there ara few instances in which genetic hard wired changes are desirable, but only in a very restrictive way and for specific purposes. One of those in sexual reproduction, and another in the maturation of immune cells. Any other change in genetic expression must be achieved via soft re-wiring. This soft re-wiring is done by cumulative epigenetic modifications and allows the production of distinct phenotypes from otherwise identical DNA templates.
One idea that is well established in developmental biology is the concept of precursor cell. From a statistical physics point of view it can be framed as a trajectory in the space of possible genetic states.
A soft re-wiring in this context can be thought as a transition from one genetic state to an adjacent one in the space of genetic states, or one step through one f the possible trajectories. A hard re-wiring may imply a change of the space of genetic states. A mutated cell is no longer in the same genetic space as their non-mutated progenitors. This poses the question of whether this is what is going on with mutated cells that become cancerous, and if so how many different ways are there to produce such kind of result. An intuitive answer may be, as many as different kinds of cancers can be identified. Althoug the evidence is strong in favor of genetic mutations, not all cancers must necessarily be the result of genetic mutations. It is possible that some can arise by soft re-wiring.
One last issue arises from the fact that cancers are multicellular phenomena. Tumors are not composed from a single cell type, but from a variety of cells that are in constant interaction. Abnormal behavior in the form of a tumor most likely requires the establishment of a set of abnormal (by kind, timing or both) interactions, which may in turn further abnormal re-wiring of the interacting cells. The change in the space of possible cell states originated by mutation is, in this sense, changing the space of possible tissue states by altering the trajectories on state transitions of non-mutated cells.