The frequency scaling exponent of low-frequency excitations in microscopically small glasses, which do not allow for the existence of waves (phonons), has been in the focus of the recent literature. The density of states g ( ω ) of these modes obeys an ω s scaling, where the exponent s , ranging between 2 and 5, depends on the quenching protocol. The orgin of these findings remains controversal. Here we show, using heterogeneous-elasticity theory, that in a marginally-stable glass sample g ( ω ) follows a Debye-like scaling ( s = 2), and the associated excitations (type-I) are of random-matrix type. Further, using a generalisation of the theory, we demonstrate that in more stable samples, other, (type-II) excitations prevail, which are non-irrotational oscillations, associated with local frozen-in stresses. The corresponding frequency scaling exponent s is governed by the statistics of small values of the stresses and, therefore, depends on the details of the interaction potential.