Similarities - all are types of photosynthesis. All have the same basic formula: CO2 + H2O -> C6H12O6 + O2 in which the plant uses light energy to convert Carbon Dioxide and Water into sugar and oxygen.
C3 is the most common form of photosynthesis.
Differences: In C3, the Carbon Dioxide is initially linked into 3 Carbon compounds on the way to becoming sugars. C4 initially creates 4 Carbon compounds, then converts them to sugar.
In C3 the photosynthesis occurs in most of the leaf tissues. In C4 it only occurs in special cells around the leaf veins (this special structure is called Kranz anatomy).
In C3 and C4 the stomata (leaf pores) are open during the day for gas exchange, which allows water to be lost from the leaves. In CAM plants, the stomata are closed during the day to prevent water loss (CAM plants are typically cacti and other desert-adaptedplants). In CAM plants, CO2 is captured and stored overnight as crassulacean acid (CAM = Crassulacean Acid Metabolism). In the daytime the CO2 is released so photosynthesis can occur without opening the stomata.
C4 plants have a special molecule called PEP carboxylase which helps the plant capture CO2 more efficiently and deliver it directly into the photosynthetic process. c4 plants are generally better able to handle low CO2 levels than C3 plants.