Wouldn't it be to just define the categories by their effect on up and down axle movement?
1) For traction bars, the axle follows a path defined by the suspension that is divorced from the traction bar.
2) For ladder bars, the axle rotates around an arc defined by the front mounting point of the ladder bar.
3) For parallel linkages (4-bars), the axle moves up and down with no rotation.
Defining it this way frees you from trying to categorize creative suspension designs. Just determine the effect on the axle movement should put a suspension in one of the categories.