if you look at the code example carefully in your book you will see things like
// Keep an eye out for this variable name okay?
private int myprivateVar = 1;
// this is a property, its a variable declaration that LOOKs like a function but its not.
// it gets a value of a private variable or changes it.
// myprivateVar is used in these braces
and it is used like so:
className.Name = "Jim Carrey"
string name = className.Name.ToString() // you may or may not need ToString()
and there you have it, as far as fields go... i would say they are variables that affect the behavior of a class like... lets say you had a class controlling how many monsters to spawn behind the player.
cMonsterSpawner.NumberToSpawn = 5;
now i might be a little bit ignorant but to me they are almost the same things. almost.