  We discuss and compare two different approaches to the notion of
Mishchenko--Fomenko subalgebras in Poisson-Lie algebras of finite-dimensional
Lie algebras. One of them, commonly accepted by the algebraic community, uses
polynomial $\Ad^*$-invariants. The other is based on formal $\Ad^*$-invariants
and allows one to deal with arbitrary Lie algebras, not necessarily algebraic.
In this sense, the latter is more universal.
