As I have seen several times of the using of those two words in even the same book. But I don't know what's the difference meaning between those two words.
Indispensable nutrients (including amino acids) are those without which life is impossible. Indispensable nutrients that cannot be internally produced, but must be consumed from some external source, are called essential.
"Essential" is a scientific term of art in nutrition (i.e. it has a fixed, universally understood meaning); "indispensable" is not. As a result, the two are sometimes used interchangeably.