select clipping mask area

As these are Shape layers you can get a precise selection of the intersecing area.

Unclip the red ellipse from the grey elipse

Select the Shape Selection tool (black arrow)

Select the grey ellipse layer and copy (Ctrl C)

Now select the red ellipse layer and paste (Ctrl V)

Set Path Options to Intersect Shape Areas in the Options bar 

Merge Shape Components and you are done. Plus you still have a vector graphic.

Use selection keyboard mods on the layers: alt-click the grey layer to select it, then ctrl-alt-shift the red layer to subtract the grey.

Like this Magic wand intersect.

It is also possible toe select the white area and the gray area.

At least three clicks are required.

It is also possible to select that gray area and also possible to select the white area.  However, the clipping mask is the full circle gray area. You can select that also. The red area is the area of the layer that was not clipped by the  clipping mask.  The white area is the layer area part that was clipped by the clipping mask