  L\'evy flights and L\'evy walks serve as two paradigms of random walks
resembling common features but also bearing fundamental differences. One of the
main dissimilarities are discontinuity versus continuity of their trajectories
and infinite versus finite propagation velocity. In consequence, well developed
theory of L\'evy flights is associated with their pathological physical
properties, which in turn are resolved by the concept of L\'evy walks. Here, we
explore L\'evy flights and L\'evy walks models on bounded domains examining
their differences and analogies. We investigate analytically and numerically
whether and under which conditions both approaches yield similar results in
terms of selected statistical observables characterizing the motion: the
survival probability, mean first passage time and stationary PDFs. It is
demonstrated that similarity of models is affected by the type of boundary
conditions and value of the stability index defining asymptotics of the jump
length distribution.
