  This commentary considers non-standard analysis and a recently introduced
computational methodology based on the notion of \G1 (this symbol is called
\emph{grossone}). The latter approach was developed with the intention to allow
one to work with infinities and infinitesimals numerically in a unique
computational framework and in all the situations requiring these notions.
Non-standard analysis is a classical purely symbolic technique that works with
ultrafilters, external and internal sets, standard and non-standard numbers,
etc. In its turn, the \G1-based methodology does not use any of these notions
and proposes a more physical treatment of mathematical objects separating the
objects from tools used to study them. It both offers a possibility to create
new numerical methods using infinities and infinitesimals in floating-point
computations and allows one to study certain mathematical objects dealing with
infinity more accurately than it is done traditionally. In these notes, we
explain that even though both methodologies deal with infinities and
infinitesimals, they are independent and represent two different philosophies
of Mathematics that are not in a conflict. It is proved that texts
\cite{Flunks, Gutman_Kutateladze_2008, Kutateladze_2011} asserting that the
\G1-based methodology is a part of non-standard analysis unfortunately contain
several logical fallacies. Their attempt to prove that the \G1-based
methodology is a part of non-standard analysis is similar to trying to show
that constructivism can be reduced to the traditional mathematics.
