The conventional representation of planar cartesian coordinates has the positive x-axis running to the left, the positive y-axis upwards.
In three dimensions, if a two dimensional graph were placed on a table in front of the observer, the positive x-axis would still run leftwards, but the y-axis would also be horizontal, running away from the observer. In perspective from a normal seating arrangement, that would still be slightly upwards; the axis would be invisible if the projection were made along the y-axis with the origin at eye-level.
The positive z-axis would run upwards, supplanting the two-dimensional y-axis. The difference in viewpoint corresponds to thinking of a two dimensional graph as being mounted on a wall, whereas the x-y portion of a three dimensional graph lies horizontally, as if placed on the table.
The choice of perspective or isometric drawings is one of taste. An architect would probably prefer a perspective view, according to the way an object would appear to a client. An engineer would probably prefer to measure true distances from the drawing, leaving matters of appearance to the imagination. GEOM uses parallel projection, adopting the second alternative; projections are made by suppressing the y-coordinate.