What is the difference between a "system" and an "organization"?

Answer 1

System:
[1]A group of interacting, interrelated, or interdependent elements forming a complex whole.
[2] A functionally related group of elements, especially: a. The human body regarded as a functional physiological unit. b. An organism as a whole, especially with regard to its vital processes or functions. c. A group of physiologically or anatomically complementary organs or parts: the nervous system; the skeletal system. d. A group of interacting mechanical or electrical components. e. A network of structures and channels, as for communication, travel, or distribution. f. A network of related computer software, hardware, and data transmission devices.
[3] An organized set of interrelated ideas or principles.
[4] A social, economic, or political organizational form.
[5] A naturally occurring group of objects or phenomena: the solar system.
[6] A set of objects or phenomena grouped together for classification or analysis.
[7] A condition of harmonious, orderly interaction.
[8] An organized and coordinated method; a procedure. See Synonyms at method.
[9] The prevailing social order; the establishment. Used with the: You can't beat the system.

Organization:
[1] a. The act or process of organizing. b. The state or manner of being organized: a high degree of organization.
[2] Something that has been organized or made into an ordered whole.
[3] Something made up of elements with varied functions that contribute to the whole and to collective functions; an organism.
[4] A group of persons organized for a particular purpose; an association: a benevolent organization.
[5] a. A structure through which individuals cooperate systematically to conduct business. b. The administrative personnel of such a structure.

So in some usages, they can be considered synonymous. See especially "system " #1 and "organization" #2 & 3.