  We find the precise relationship between the loop gas method and the matrix
quantum mechanics approach to two-dimensional string theory. The two systems
are distinguished by different target spaces ($\Z$ and $\R$, respectively) as
far as {\it observables} are concerned. We argue that target space loop
correlators should coincide in the two models and demonstrate this for a number
of examples. As a consequence some interesting generic observations about the
structure of two-dimensional string theory may be made: Restricting to a
discrete target space leads to {\it factorization} of amplitudes and thus to
very simple sewing rules. It is also demonstrated that the restriction to the
discrete target space still allows to calculate the correlation functions of
tachyon operators in the unrestricted theory.
