You walk in to a McDonald's and are presented with a menu. There are many different items on the menu, including a Big Mac, a Quarter Pounder w/Cheese, a hot apple pie, and the ever-disgusting Filet-O-Fish.
You walk up to the counter and order a Big Mac. You are presented with with a 3-layer bun, 2 "all beef" patties and some special sauce, all enclosed in a piece of paper.
The person behind you orders the same thing, and they are given their own burger. You both sit down and start to eat. You eat yours very quickly, but your neighbor barely touches his.
The 3rd person in line orders the Apple Pie, and they are given something entirely different. A little semi-cylindrical pastry filled with something resembling apples.
In this analogy, the printing on the menu is the storage duration, and the type of burger itself is akin to the object lifetime. Two different storage durations were selected; the Big Mac and the Apple Pie. Three objects were produced as a result: two burgers and one pastry. Two of those objects have the same general makeup, even though they are two distinct burgers, but the third is different. Two storage durations, three objects.
Your quote:
Lifetime of an object is equal to or is nested within the lifetime of
its storage.
Is not a definition for "lifetime" or "storage duration", but simply relates the two. It tells you, given a "storage duration" of X you can expect a lifetime of Y.
In that sense, the two terms are really twos sides of the same coin. A particular storage duration yields a particular lifetime.
This is elaborated on in the (C++03) Standard:
3.8 Object Lifetime
1/The lifetime of an object is a runtime property of the object. The
lifetime of an object of type T begins when: — storage with the proper
alignment and size for type T is obtained, and — if T is a class type
with a non-trivial constructor (12.1), the constructor call has
completed. The lifetime of an object of type T ends when: — if T is a
class type with a non-trivial destructor (12.4), the destructor call
starts, or — the storage which the object occupies is reused or
released.
3.7 Storage Duration
1/Storage duration is the property of an object that defines the minimum
potential lifetime of the storage containing the object. The storage
duration is determined by the construct used to create the object and
is one of the following: — static storage duration — automatic storage
duration — dynamic storage duration