Rectilinear figures are those which are contained by straight lines, trilateral figures being those contained by three, quadrilateral those contained by four, and multilateral those contained by more than four straight lines.
Euclid classifies rectilinear figures by their number of sides in this definition. Classifying them by their number of angles could lead to complications since an angle has to be less than two right angles, and a non-convex figure would have an internal angle greater than two right angles.
The modern English names, however, are based an the number of angles (except quadrilateral): triangle, pentagon, hexagon, heptagon, octagon, etc. From pentagon on up these names derive from the Greek, but they're rarely used past octagon.