$S_{0.5}$ vs $K_m$ values in enzyme kinetics
This expands my comment on the question to an answer. 

If an enzyme exhibits Michaelis-Menten kinetics, then it is valid to define a KM and this equates to the substrate concentration when reaction velocity is 0.5 * Vmax.

However, many enzymes do not exhibit Michaelis-Menten kinetics. One example is when the enzyme shows a co-operative response to substrate concentration. In these circumstances the substrate concentration when reaction velocity is 0.5 * Vmax is still a useful parameter, but there is no KM.

See this paper for a discussion of the kinetic properties of the glucokinase of pancreatic &beta; cells, which acts as the glucose sensor. This enzyme shows positive co-operativity with respect to its substrate glucose, and the authors develop a kinetic analysis in terms of various parameters. These include an S0.5 value for glucose, but a KM value for ATP (presumably because the kinetics with respect to ATP are simple Michaelis-Menten).