There aren't two kinds of Hess cycles? I don't think you have understood it correctly. Lets say for example we have a reaction where A+B goes to C. In order to find the enthalpy of this reaction we will use the cycle. If we knew how to go directly from A and B to C then we would not need to apply the Hess Cycle, however we don't. However we do know that A and B break down into D and E, and the reaction of D and E also makes C. We know the enthalpy of formation for D and E, we also know the enthalpy of formation for C from D and E. Therefore, we find the enthalpy of A+B-->C by using the enthalpy of A+B--->D+E with the addition of enthalpy from D+E--->C.
This may be a confusing reply, but I hope it helps