Chemistry - What is the difference between "atomic hydrogen" and "nascent hydrogen"?

Is your book by chance very old? From the Wikipedia entry for "nascent hydrogen":

Nascent hydrogen is purported to consist of a chemically reactive form of hydrogen that is freshly generated, hence nascent. Molecular hydrogen ($\ce{H2}$), which is the normal form of this element, is unreactive toward organic compounds, so a special state of hydrogen was once invoked to explain certain kinds of hydrogenations. Mechanistic understanding of such reactions is now available, and the concept of nascent hydrogen is discounted, even ridiculed.

Then, by example of how this concept came to be:

Reductions of esters to give alcohols using a mixture of sodium and alcohols is called the Bouveault–Blanc reduction. It is an old reaction that has largely been superseded by alternative methods. At the time of popularity, the process caused much puzzlement because esters are unreactive toward hydrogen. It was also known that sodium reacts with alcohols to release $\ce{H2}$. it was concluded that some freshly generated ("nascent") hydrogen was responsible for this remarkable reaction. Subsequent studies have shown that this reaction proceeds via electron-transfer from metallic sodium to the ester substrate followed by protonation of the reduced intermediate. The evolution of hydrogen by the reaction of sodium and alcohol is purely a competitive reaction, the sole benefit being that in the presence of sufficient alkoxide, the sodium/alcohol reaction slows.

So in general, at least toward organic compounds, your relative reactivities of hydrogen species are correct if you take out "nascent" hydrogen so that:

$$\ce{H2} \lt \rm atomic~hydrogen$$