  The generalized deformed oscillator schemes introduced as unified frameworks
of various deformed oscillators are proved to be equivalent, their unified
representation leading to a correspondence between the deformed oscillator and
the N=2 supersymmetric quantum mechanics (SUSY-QM) scheme. In addition, several
physical systems (two identical particles in two dimensions, isotropic
oscillator and Kepler system in a 2-dim curved space) and mathematical
structures (quadratic algebra QH(3), finite W algebra $\bar {\rm W}_0$) are
shown to possess the structure of a generalized deformed su(2) algebra, the
representation theory of which is known. Furthermore, the generalized deformed
parafermionic oscillator is identified with the algebra of several physical
systems (isotropic oscillator and Kepler system in 2-dim curved space,
Fokas--Lagerstrom, Smorodinsky--Winternitz and Holt potentials) and
mathematical constructions (generalized deformed su(2) algebra, finite W
algebras $\bar {\rm W}_0$ and W$_3^{(2)}$). The fact that the Holt potential is
characterized by the W$_3^{(2)}$ symmetry is obtained as a by-product.
