In contrast to overtaking interactions, head-on collisions between two electrostatic solitons can be dealt with only by use of an approximate method, which limits the range of validity but offers valuable insights. Treatments in the plasma physics literature all use assumptions in the stretching of space and time and in the expansion of the dependent variables that are seldom, if ever, discussed. All models force a separability to lowest order, corresponding to two linear waves with opposite but equally large velocities. A systematic exposition of the underlying hypotheses is illustrated by considering a plasma composed of cold ions and nonthermal electrons. This is general enough to yield critical compositions that lead to modified rather than standard Korteweg-de Vries equations, an aspect not discussed so far. The nonlinear evolution equations for both solitons and their phase shifts due to the collision are established. A Korteweg-de Vries description is the generic conclusion, except when the plasma composition is critical, rendering the nonlinearity in the evolution equations cubic, with concomitant repercussions on the phase shifts. In the latter case, the solitons can have either polarity, so combinations of negative and positive solitons can occur, contrary to the generic case, where both solitons necessarily have the same polarity.