Thermoset epoxies are widely used due to their excellent properties, but conventional epoxies require a complicated and time-consuming curing process, and they cannot self-healed, which limits their applications in self-healing materials. Extrinsic and intrinsic self-healing materials are applied in various fields due to their respective characteristics, but there is a lack of comparison between the two types of healing systems. Based on this, a thiol-epoxide click reaction catalyzed by an organic base was introduced to achieve the efficient preparation of thiol-epoxy. Furthermore, tung oil (TO)-loaded microcapsules were introduced into the thiol-epoxy matrix of dynamic transesterification to obtain a TO/TMMP-TMTGE self-healing composite with an intrinsic-extrinsic double-healing system. For comparison, a TMMP-TMTGE self-healing material with an intrinsic healing system was also prepared, which contained only thiol and epoxy curing chemistries. The effect of the core/shell ratio on the morphology, average particle size, and core content of TO-loaded microcapsules was studied. It was found that when the core/shell ratio was 3:1, the average particle size of the microcapsules was about 99.8 μm, and the microcapsules showed good monodispersity, as well as a core content of about 58.91%. The differential scanning calorimetry (DSC) results showed that the TO core was successfully encapsulated and remained effective after encapsulation. Furthermore, scanning electron microscopy (SEM), atomic force microscopy (AFM), tensile tests, and electrochemical tests were carried out for the two types of self-healing materials. The results showed that the TO/TMMP-TMTGE composite and TMMP-TMTGE material both had self-healing properties. In addition, the TO/TMMP-TMTGE composite was superior to the TMMP-TMTGE material due to its better self-healing performance, mechanical strength, and corrosion protection performance.