Russell and Norvig are not saying that searching and planning are different things. In fact, in the section I think you're taking about (in Chapter 10 of the Blue Edition) they say exactly the opposite: A planning problem can be reduced to a search problem.
But, the plan expressed as a search may have a monstrously large search space. In the book example, there are 10^10 different possible actions, and with an uninformed search technique the computer does not "know" that buy(x) results in have(x) even though this is trivially obvious to a human being. Thus, even the search space of single-action plans is huge. That sounds stupid, but it is the definition of uninformed search.
As a result, planning algorithms that actually work require some algorithmic and/or heuristic cleverness, which the rest of that chapter goes on to describe. In the book example, the improved search reasons backwards from the goal of have(x), performs some first-order-logic schema listing using the buy(x) vs have(x) connection and derives the correct action.
As a side note, I am a great fan of Russell and Norvig's book, and their work in general. But I found the planning chapters to be a little bit weak. Professors Lozano-Perez and Kaelbling have their lecture notes from a class using a previous edition of the book online. Their notes are very detailed, with examples. I found them to be an excellent supplement when I was studying this material:
http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-825-techniques-in-artificial-intelligence-sma-5504-fall-2002/index.htm