  A construction of Gelfand-Tsetlin type base vectors in a finite-dimensional
representation of $\mathfrak{sp}_{2n}$ was firstly obtained in 60-th by
Zhelobenko. But the final construction was obtained only in the year 1998 by
Molev, who gave a construction of Gelfand-Tsetlin type base vectors and derived
formulas for the action of generators of the algebra in this base. These two
approaches use different ideas.
  In the present paper we compare these two approaches. Also we show that the
Molev's base vectors can be obtained using a construction based on a relation
between restriction problems $\mathfrak{sp}_{2n}\downarrow\mathfrak{sp}_{2n-2}$
and $\mathfrak{gl}_{n+1}\downarrow\mathfrak{gl}_{n-1}$, analogous to the
construction giving the Zhelobenko's base.
