Different types of central relaxation oscillations are observed in the presence of ECH depending on the location of the deposited power. In the TCV tokamak, normal sawteeth, i.e. triangular sawteeth similar to ohmic sawteeth, and saturated sawteeth are observed with central ECH power deposition, while giant sawteeth and 'humpback' oscillations occur when heating close to the sawtooth inversion surface of the local soft X ray emissivity. New measurements with high temporal resolution show that the crash phase of these sawtooth types is accompanied by a reconnection process associated with an m/n = 1 resistive internal kink mode. After the sawtooth crash, full magnetic reconnection is observed in normal and in saturated sawteeth, while for giant and humpback sawteeth the reconnection process is incomplete and poloidally asymmetric temperature profiles persist after the crash. The detailed dynamics of the magnetic island associated with the resistive internal kink mode are described by a displacement function which is inferred from the experimental data. In normal sawteeth, the kink mode is destabilized just before the crash, while in all other sawtooth types a magnetic island exists for a significant fraction of the sawtooth period. The different types of sawteeth have been simulated using a numerical code based on a theoretical model which describes the evolution of the electron temperature in the presence of localized heat sources and of a magnetic m/n = 1/1 island.