Question on ray_color function (book 1)

[polaris]

In the different implementations of the ray_color function, the target vector is calculated by adding the random vector to rec.p. However, rec.p is subtracted on the following line. For example:

point3 target = rec.p + random_in_hemisphere(rec.normal);
return 0.5 * ray_color(ray(rec.p, target - rec.p), world, depth - 1);

This seems excessive. Isn't the following code doing the same without rec.p?

point3 target = random_in_hemisphere(rec.normal);
return 0.5 * ray_color(ray(rec.p, target), world, depth - 1);