Quantum field theory is, very broadly, the area of physics that combines classical field theory and quantum mechanics. Its a generalization of Quantum Mechanics that enables us to quantize and study "richer" objects.
Some would say that within this framework, it also combines special relativity, but this corresponds to only a subset of quantum field theories, such as the Standard model. Actually, the Standard model is a model within the framework that is called Quantum field theory. In condensed matter physics, special relativity is not needed in general (although this might have some exceptions, such as in the case of some effective theories). Actually, the fields we quantise, and indeed our whole theory, can be invariant under different transformations which would distinguish the typical QFTs found in high-energy physics which are Lorentz invariant. One such QFT is conformal field theory, which is just a QFT that's invariant under the so-called conformal transformations.
So, the explanation here is clear: quantum field theory is a marriage between classical field theory and quantum mechanics. Any extra ingredient makes it more specific. If you alo combine special relativity, you get a Lorentz invariant QFT, something that is still pretty general; there is still the action, which defines a model out of the framework. You choose the fields and their interactions. A specific set of fields and interactions, along with the appropriate symmetries, such as Lorentz invariance, gets you the Standard Model.
Now, if you want conformal invariance (which includes things such as scale invariance) instead, you get a conformal field theory. This is still not a rigid model, it is still a framework in that lots of fields and their interactions can be conformally invariant.
The same happens in condensed matter physics. There you do not generally have Lorentz invariance (hence, neither Poincare invarince), so your framework is non-relativistic. Once you figure out your fields and their interactions etc, then you get a model. That is why there is such a broad set of theories in condensed matter (models describing superconductors, others describing Hall effects, etc).