Your general impression is correct.
The first term (能率, nōritsu) generally applies to how much can be gained with in a set time period. It is used more abstractly and generally, often to refer to an improvement in performance of a task at work, as in statements like "using a computer is more efficient".
Also, this term is used in physics to refer to a moment, although in the material I've seen on that topic, モーメント (mōmento) is more common.
The second term (効率, kōritsu) more often applies to the operational efficiency or effectiveness of machinery or equipment, or to the amount gain or benefit obtained with respect to effort applied. In concrete terms, 効率 tends to be used to describe the performance of various types of machinery or equipment as regards, for instance, energy efficiency, power consumption, or output.
The second term (効率) is widely used in technical literature, research papers on topics such as electrical engineering, power electronics, and mechanical engineering, and anywhere that the performance or a device or apparatus is being measured and evaluated.