The relationship between search and planning is not made clear in the material you are reading, which is one of many reasons MIT doesn't use AI by Russell and Norvig anymore. It isn't the modern approach now and wasn't in the best survey course textbook when it came out, but it was politically correct with the faculty then. An online and updated version of Artificial Intelligence, by Patrick Henry Winston, 1992, Addison-Wesley is what MIT's Artificial Intelligence Lab (course 6.034), taught by Winston, uses now.
A few things can be said about searching as a general activity.
- There is a space to search.
- There is a way to test the space for the presence of something.
- The something must be present for the search to succeed.
- There may or may not be hints as to whether the searcher is getting close.
- More then one searcher may search in parallel.
- There are different ways to decide the order of what to test.
- Searching the same unique possibility more than once is a waste of time.
These last two items are related and lead to DFS and BFS and the others a more complete list and treatment of which can be found here: Which Algorithm is best for Robots?.
A few things can be said about planning as a general activity.
- Planning is done to attain a goal or goals.
- Planning often involves avoiding some specific conditions.
- During planning, decisions are made to optimize the attainment of the goals and avoid the conditions specified.
- Resources are utilized to execute the planning operations.
- Resources are utilized to execute the plan.
- The conditions may change during the execution of the plan requiring plan adjustment.
It is reasonable to try to unify these two things into a single concept this way.
- The specified conditions to avoid in planning are the limits of the search space for the equivalent search.
- The goal or goals of the plan can be formulated in the test for search success.
- The attainment plan is much like the search strategy with the aggregated goal as the thing to find.
This is all based on the idea that the search space is an n-dimensional space, that some function of each location in that n-dimensional space has a value, and maximizing that value is a way of mathematically representing both the goals of the plan and the success of the search.
Here's where the reason evaporates and the unification of searching and planning requires bending the meaning of the words to succeed. Plans may involve highly abstract things such as deciding whether or not to use the word Modern in the subtitle of a book with the goal of selling the book and also attracting people to MIT's new curriculum. Yet the search would be what? Searching for a way to make some royalties and attract students?
- The execution of plans can involve multiple people, but the planning itself is generally not easily done in parallel. Those who have worked on committee know this to be true. Planning is not a highly distributable operation. Searching is the opposite. It is not a very efficient centralized operation.
- When the conditions change (in the above case the field of AI and what is considered modern) a plan can be and is often if not usually modified to match the change in conditions. These changes may include changes to the most strategic and general logical structures in the plan. Searching can be modified if it is parameterized to do so or a plan is developed to switch searching strategies in such a way that already tested spaces are not retested unless they are marked as modified but, but that is a stretch of the meaning of searching.
In summary, for very low cases planning operations can be thought of as a search for the best plan based on some criteria. For those cases, searches proceed according to some search plan, but even at that low level, they are distinct. For more complex cases involving cognition and reasoning, there is very little in common between planning and searching.
If all these things are understood and then the textbook is read, the material may make more sense and the comprehension may not only cause the correct answer to come to mind but the student may smile because the textbook is old and some of its presentation is counter-intuitive because its just incorrect in the light of the maturing field of AI.