This is different than the questions concerning two walls of fire being in the exact same place, what I'm asking if you have concentric walls that never touch, but are in the same area, are they counted as being in the same area of effect? See picture for reference.
A spellcaster cannot maintain concentration on more than one spell at a time, so we're going to answer this question assuming there are multiple casters.
To start, we'll look at wind wall as an example spell, then see if we can apply any lessons learned more generally. In this spell, we can create a wall up to 15 feet high, 50 feet long, and one foot thick, in any configuration, so long as it makes a single continuous path along the ground. If we made a circle with an internal diameter of 5 feet, we'd fall well within those guidelines. Anything passing through the 1-foot thick wall would be within its area of effect.
A second caster places a second wind wall within the first, giving their wall an internal diameter of 3 feet (and thus an external diameter of 5 feet). If these walls are not touching, do their areas of effect overlap? By definition, no. The walls themselves are the areas of effect, so if the walls don't touch, they can't overlap.
Does this rule apply to all walls made via spell? It certainly would hold true for wall of thorns, wall of stone, wall of ice, and wall of force, though for several you would have to shape a square rather than a circle, and the sizes would depend on the thickness of the wall created. Wall of fire is a special case, as its area of effect extends beyond the wall itself. In that one instance, the areas of effect would overlap, and even then only if both walls were facing the same direction. In that instance the previously discussed ruling applies.
And thus we have a general rule: if the area of the wall itself is the area of effect, then two non-touching walls do not have overlapping areas of effect. If the area of effect extends beyond the wall itself, then they can.