Thaumaturgy

    One crucial difference in Thaumaturgy between 2dn Edition and Version Three is it's dependence on external sources of power which is what allows it to be accessible to mortals. Exalted and other supernaturals cannot circumvent this restriction. Thaumaturgy depends on use of esoteric materials and objects. Powering magic through inner Essence is called sorcery. Unlike sorcery it's effectiveness is somewhat limited and cannot perform totally supernatural feats, although it is significantly realty bending, being able to restore the dead to life under carefully controlled circumstances.
    On the material requirements for Thaumaturgy mere resources are not an accurate indication of the objects needed to perform a ritual. Objects for a ritual are often very specific and may even be unique requiring a small quest to acquire them (such as the Heart of Dambala in Bride of Chucky.)

    Science is comparable to Thaumaturgy. It involves using materials in a predictable, formulaic way. A lot of science fiction involves use of some extremely powerful energy source. Those are hearthstones. Iron Man had an arc reactor. Power armour has hearthstone sockets

Magitech and Thaumaturgy

    Thaumaturgical facilities like oil refineries. During the First Age Solars put thaumaturgical engineering onto an industrial scale. Including weapons engineering. Artefacts made the Exalted even more mighty, but thaumaturgical weapons armed their armies. Magitech is a half-way point between artefacts ad engineering. It works mechanically but needs to be infused with Essence to become activated. The world was dotted with factories producing thaumaturgical items during the First Age. As time went on ore and more of them were uesd for producing weapons and other military hardware as the Exalted became more and more antagonistic towards eachother.
   Witht the requirement of Essence attunement and even hearthstone power, it was inadvisable to use magitech for disposable weapons but thaumaturgy was a viable option.
   Producing these weapons however was far from safe, especially the more dangerous ones. These were also difficult to produce and their place of manufacture, sometimes their very existence were kept secret. Due to the dangerou, unstable nature of the substances often involved, research and production were usually expensive with a large proportion of resources spent on exotic safety measures.
   The energy used in magitech came from the power of Creation itself. Using Elemental and Celestial enegies they powered the magitech devices that made the First Age an unparalleled era of civilisation and later decadence.