  Discrete mechanics proposes an alternative formulation of the equations of
mechanics where the Navier-Stokes and Navier-Lam\'e equations become
approximations of the equation of discrete motion. It unifies the fields of
fluid and solid mechanics by extending the fields of application of these
equations to all space and time scales. This article presents the essential
differences induced by the abandonment of the notion of continuous medium and
global frame of reference. The results of the mechanics of continuous medium
validated by fluid and solid observations are not questioned. The concept of
continuous medium is not invalidated, the discrete formulation proposed simply
widens the spectrum of the applications of the classical equations.
  The discrete equation of motion introduces several important modifications,
in particular the fundamental law of the dynamics on an element of volume
becomes a law of conservation of the accelerations on an edge. The acceleration
considered as an absolute quantity is written as a sum of two components, one
soledoidal the other irrotational according to a local orthogonal
Helmholtz-Hodge decomposition. The mass is abandoned and replaced by the
compression and rotation energies represented by the scalar and vectorial
potentials of the acceleration. The equation of motion and all the physical
parameters are expressed only with two fundamental units, those of length and
time. The essential differences between the two approaches are listed and some
of them are discussed in depth. This is particularly the case with the known
paradoxes of the Navier-Stokes equation or the importance of inertia for the
Navier-Lam\'e equation.
