Multicellular organisms begin life as single cells called zygotes or spores, depending on the species. This cell then divides and multiplies, creating additional cells. Differentiation is the process by which the cells take on their specific functions. Morphogenesis is the process by which an organism takes on its shape.
One difference between differentiation and morphogenesis is the presence of signals. Differentiation is always triggered by some signal from the cell's environment. Signals include changes in light, physical stimulation, chemicals and temperature. In contrast, no set events trigger morphogenesis.
Even though cells continue to replicate throughout a multicellular organism's lifetime, differentiation and morphogenesis typically occur when the organism is in the process of growing from the original zygote or spore. In this case, differentiation happens before morphogenesis is complete. This is because differentiation allows morphogenesis to happen.
Compared to morphogenesis, differentiation is an isolated process. It occurs in response to specific signals that occur after a process called determination is complete. Cell determination essentially programs the nonspecific cell so that it will become a certain type of cell. Morphogenesis is a comprehensive process that is complete when the entire organism takes shape. Differentiation is an isolated part of the process of morphogenesis.
Consider a developing human embryo. Differentiation makes sure that some cells will turn into blood cells and that other cells will create the veins and arteries that carry blood. Differentiation also creates cardiac cells for the heart and neurological cells for the brain. Morphogenesis determines that the veins and arteries will be tubular structures found throughout a person's body, that the heart will be located near the center of the chest and that the brain will be found within a person's skull atop the body.