My suggestion is you throw this book away, and use only "good books".
Whoever wrote this book has a very confused mind.
I can vaguely guess what the author might have had in mind when he mentioned these "three types", but trying to make sense of these very confused notions would only add to your confusion, not reduce it.
Also, while the revolution of the Earth around the Sun does involve inertia, the overall motion is certainly not exclusively due to inertia.
Just as a matter by curiosity (certainly not to buy it) what are the title and author of this book ?
EDIT
Maybe I should have given you more details earlier.
The inertia that, when no force is applied, keeps at rest a body at rest is the same that guarantees a body in motion "perseveres" in this motion at the same speed in the same direction. So what your book call "inertia of rest", "inertia of motion" (constant value of the speed in meters per second?) "inertia of direction" (which, combined with the previous one, is the only meaningful thing for a physicist, conservation of the "physical speed" which means both direction and value in meters per second). Distinguishing them as three "types of inertia" makes absolutely no sense.
Now about the Earth and the Sun. Before <PERSON> (thank you, user4574), people believed the Sun went around the Earth. Now we know that it is the contrary, the Earth goes around the Sun. But this motion, called "revolution" takes a whole year and in combination with the tilt of the Earth's axis is responsible for the seasons. 393
This motion does involve inertia, but also a force. It is the interaction of this force, the gravitation of the Sun, and the inertia of Earth that is responsible for it, not just some "rotational inertia" that by itself would keep the Earth to go around the Sun because it is now rotating around it.
There is really, however, such a thing as "rotational inertia". But not to go round another object: to keep an object rotating around itself (technically, around it own axis), like a rotating top, to keep rotating indefinitely if no (momentum of) force is applied on it. I am not going to elaborate on the notion of "momentum of force".
And indeed the Earth does rotate around its own axis. Not once a year but once a day. This is why we see the Sun rise and set every day. This daily motion does not mean that the Earth rotates around the Sun but rather rotates around its own axis, once a day.
And this daily motion, yes, is purely due to inertia, a different sort of inertia than the first one, technically called "conservation of angular momentum", but you can think about it, if you want, as a "rotational inertia" though to my knowledge nobody uses this term.
So yes, sunrise and sunset are phenomenons due to inertia, to the fact that the Earth keeps turning around its own axis, like a rotating top.
But it was not at all clear that you were referring to this daily motion in your question, since you were mentioning "going round the Sun", which I understood as the year-long revolution, which is not purely due to inertia. 393