What are ordinary mass-terms (of neutrinos)?
What is the meaning of ordinary mass terms?
The "ordinary mass terms" in the quoted paper (see-saw mechanism) would stand for Dirac mass terms, which couple active left-handed neutrinos $\nu_L$ (the isospin "up" part of the electroweak $SU(2)$ left-handed neutrino-electron doublets) to the sterile right-handed neutrinos $\nu_R$ (as $SU(2)$-singlets): $$ m (\bar{\nu}_L\nu_R + \bar{\nu}_R\nu_L). $$
The "non-ordinary mass terms" would mean Majorana mass terms, which couple the sterile right-handed neutrino $\nu_R$ to the charge-conjugate of itself $\nu^c_R$: $$ M \bar{\nu}_R\nu^c_R. $$
The "ordinary" Dirac mass $m$ is of the eletroweak symmetry breaking scale, while the "non-ordinary" Majorana mass $M$ is of the much higher see-saw (or grand unification) scale . In the usual scheme of the sea-saw model, the tiny neutrino mass is the resultant effective mass $m_{\nu}$ with scale: $$ m_{\nu}\sim \frac{m^2}{M}. $$