What's the difference between the magnetocaloric effect and the thermomagnetic one? I do not really understand the difference between the magnetocaloric effect and the thermomagnetic one. From what I gather from Wikipedia, one is just the reverse of the other. Namely, the influence of an applied magnetic field to the temperature of the sample is due to the magnetocaloric effect, while a change in the magnetization of the sample due to a temperature change is due to the thermomagnetic effect. 
But if that is so, then the naming is arbitrary, for it corresponds exactly to the same physical process. Namely that $\vec M$ and $T$ are interlinked and changing either one will automatically change the other one. It's a single effect, to me.
However there are papers that seem to make a difference, such as this one. But it isn't clear to me at all where the difference really lies. I suspect there is a real difference, but I do not see it.
Thus the question is, what are the differences between the magnetocaloric and the thermomagnetic effects?
 A: They are different effects, and the paper you cite confused them (there is no thermomagnetic analysis in that paper despite the title and claims).
In the magnetocaloric effect, a material is subjected to an applied magnetic field, which will modify the temperature of the sample (roughly uniformly if the material is isotropic and homogenous). Physically, this is due to a change in entropy when the spin of the magnetic material align with the applied field.
On the other hand, with a thermomagnetic effect such as the Nerst effect or its "reverse", the Ettingshausen effet, you either start with a temperature gradient and an applied magnetic field, which will create an emf. Or you start with a current and an applied B field, which will create a temperature gradient. Physically, it can be explained by using the Lorentz force applied to moving charges, and with having in mind that a temperature gradient is responsible for a "diffusion" of charges like with the thermolectric effect. So, it is quite a different picture than with the magnetocaloric effect.
Note that there exist a spin Seebeck effect, also a spin Thomson effect, etc. but they are not equivalent to the magnetocaloric effect, either.
