  The various relations between $q$-deformed oscillators algebras and the
$q$-deformed $su(2)$ algebras are discussed. In particular, we exhibit the
similarity of the $q$-deformed $su(2)$ algebra obtained from $q$-oscillators
via Schwinger construction and those obtained from $q$-Holstein-Primakoff
transformation and show how the relation between $su_{\sqrt{q}}(2)$ and Hong
Yan $q$-oscillator can be regarded as an special case of In\"{o}u\"{e}- Wigner
contraction. This latter observation and the imposition of positive norm
requirement suggest that Hong-Yan $q$-oscillator algebra is different from the
usual $su_{\sqrt{q}}(2)$ algebra, contrary to current belief in the literature.
