If you consider an ideal gas without any mean motion, then at the molecular level all you have is molecular motion (there is no potential between them, except that associated with hard spheres), and therefore every property definable for an ideal gas must have its origin in that motion. But then the procedure for calculating any particular property (say, internal energy) is different from that for another property (say, pressure; if you are thinking of a flow, then static pressure).
As @Jannick said in his comment, internal energy accounts for other kinds of energy apart from kinetic energy of molecules. However even if the ideal gas molecule is assumed to have no further structure so that its internal energy is completely accounted for by kinetic energy of its molecules, it is still different from pressure.
Pressure at a point is defined as normal momentum flux per unit area of an infinitesimal surface located at that point (see this). Unlike what you said, a direction is essential in defining this particular momentum flux, which direction is the normal to the area element under consideration. Only under the assumption of isotropy does this particular momentum flux become independent of any direction. Internal energy on the other hand is defined as amount of kinetic energy of molecules contained in a volume. There is no flux across some area element to be considered in this definition. As you can see, even though both properties refer ultimately to molecular motion, they, by virtue of their particular definitions, are measuring different aspects of molecular motion. In fact you can vary the two properties independently of each other.