Thermoset or thermoplastic isn't differentiated by the functional groups of the polymer per se, but rather its macroscopic phase behavior. A thermoset goes from liquid to solid irreversibly. Often heat is what causes this, but newer technologies take advantage of UV irradiation, inclusion of catalysts, or other triggering factors. Once solidied, that is it for a thermoset, its shape cannot be modified without damaging it.
A thermoplastic can be cycled between a solid at temps below the melting point and a liquid at above the melting point many times. Its shape in the solid can therefor be modified just by heating and pouring into another mould.
What causes something to be a thermoset structurally usually has to do with the presence of reactive groups pendant to the main polymer backbone. A good example is that PDMS with a small amount of pendant Si-H groups and another PDMS with small amount of vinyl groups will be combined together. They exist as a mixture of liquid polymers, but when a bit of Pt catalyst is added, the mixture will crosslink and set into a hard shape.