A dog runs toward the camera with a stick in its mouth.
There is a dog carrying a stick in it's mouth.
The dog has a stick in its mouth in both sentences, but the first has more detail.
exists e1 x1 x2 x3 x4.(n_mouth(x4) & of(x4,x2) & n_thing(x2) & n_camera(x2) & in(e1,x4) & toward(e1,x2) & with(x2,x3) & n_stick(x3) & Actor(e1,x1) & v_run(e1) & n_dog(x1))
exists p1 x1 p2 x2.((x1 = x2) & exists e1 p3 x3 x4.(exists x5.((e1 = x5) & n_mouth(x5)) & Theme(e1,x4) & Actor(e1,x3) & v_carry(e1) & in(x4,x2) & n_stick(x4) & n_thing(x3)) & n_thing(x2) & that(x2,p2) & n_dog(x2))