There are in principle two ways that two cells with the same mother cell can differentiate/specialize/diverge:
Because they are not perfect identical copies (= different internal influencing factors). I explictly don't mean "non-identical on the DNA level", but on the level of other cellular components!
Because they are exposed to different external influencing factors (chemical, mechanical).
Can it be said, which of these two reasons of cell differentiation is the more common, frequent, resp. "important"? Or does it completely depend on the (type of mother) cell and some general circumstances?
If internal factors (= non-identical copies) are an important source of differentiation, I have two (optional) questions:
How does the mother cell manage to cleave into two non-identical copies in a rather fine-tuned and determinstic way? Or is any kind of asymmetry enough?
Which is the first cell (starting with the zygote) that cleaves into two non-indentical cells, different enough to give rise to differentiation? (From this answer I believe to have learned that this might happen already after 1-4 divisions.)