Generally, initialization of a variable is the first assignment after declaration, as variables are not automatically initialized. Subsequent assignments are just assignments.
void foo() {
int i;//not initialized.
}
Except for fields, which are variables declared in a class or struct. These are initialized to their default values just before the constructor is called for that object instance. Hence, even if you (first) assign something to a field in a constructor and that field was not initialized at declaration, it is strictly speaking assignment, not initialization. Without going into such detail, I guess many programmers do consider the first assignment of a field in a constructor as initialization though, and may use it as such in their conversations with each other. Probably this usage/habit stems from having used unmanaged languages like C/C++ where a variable contains gibberish when first declared, and hence they have to fill it with non-rubbish values (initialization).
class A {
int x;//not initialized
int y = 1;//initialized here
A() {
x = 1;//strictly speaking, not initialization, just assignment.
y = 2;//was obviously initialized above
}
}
For programmers not writing compilers or languages, to be able to communicate effectively with other programmers is more important than knowing the exact terminology of the word initialization. So go ahead and use it in the meaning which everyone around you understand. You will not be wrong to explain the exact meaning though (but I probably won't for fear of exposing my pedantic tendencies).
Personally I will avoid a book that uses a term "initialization command" for variables.