This question is critical in the understanding of thermodynamics, and I think that few people makes it for fear of being considered fools and prefer just memorizing the book.
First, the systems theory defines a system as a set of parts standing in interrelations (Bertalanffy). This imply that systems have sub-systems and sub-systems have sub-sub-systems; also, that all systems belong to a supra-system, etc. But remember this: not in thermodynamics. In thermodynamics there are only two system types: the whole (also called the thermodynamic system) and the parts (the molecules, or also, the sub-systems).
The classical thermodynamics exercise sets two containers with gas molecules at different temperatures, then, we open a wall separating both containers and they become a single one, so the molecules start mixing.
In this case:
The container is the system or the whole, and the molecules are the subsystems. There it is: there are no more levels of subsystems and suprasystems. Why? Because, Clausius, Boltzmann, et.al. supposed that things are a physical fact of the universe, and this might not be the truth (to be explained at the end). Anyway, we need this false truth in order to calculate the thermodynamic variables, and this false truth simplifies things.
The first law deals with energy conservation. Where? In the whole, as the sum of the energy of the parts. The total energy of the parts (internal to each part, internal to each molecule) is not considered (now you understand why avoiding the existence of sub-sub-systems seems a good idea to simplify things).
The above principle implies that thermodynamics requires the denial of the energy and mass relativistic equivalence. If a molecule would be polymerized (split into atoms + energy [the energy of the atomic bounding]), then, a sub-system is being converted into sub-sub-systems + energy, and that would add a large complexity to thermodynamics (in fact, that's a real problem when thermodynamics is applied to chemistry). So, the first law deals only with the conservation of energy of the whole, not the conservation of energy of the parts.
The second law, (my definition of entropy and the second law, coherent with Boltzmann or Clausius: "energy tends to propagation"), deals with the dispersal of the energy within the whole, that is, the energy dispersal or propagation across the parts or sub-systems. Then, we don't talk about the entropy of the molecules, the atoms, the quarks, or the supra-system (the room, or the universe). We always talk about the entropy of the system. The target where entropy is calculated is always the system, in this configuration of a unique "system made by indivisible parts". It is the entropy of the system that always grows.
When someone says that the entropy of a refrigerator (the whole) decreases at the expense of the context (e.g. the kitchen room, which is the supra-system), it is a sort of naive application of Clausius' formulas. The intention is to say that naturally, if the fridge is cold and the exterior is hot, then, the fridge tends to increase its temperature in order for entropy to grow. But for entropy to decrease, the energy dispersal between the apples, bananas and grapes (the subsystems) in the fridge would not disperse, but concentrate into each fruit-thing. What is happening is that the fridge is just losing energy, and transferring it to the environment. What we are talking about is not the entropy of the refrigerator, but the entropy of the kitchen (or the system made by the interaction kitchen -- refrigerator). Then, the error is to say that the entropy of the refrigerator decreases. The correct statement is to say that the entropy of a kitchen reduces when a refrigerator is active (energy is concentrated outside the refrigerator, which is an amazing human achievement!). But at the expense of the entropy of the suprasystem: the universe. In order to assess the second law, the energy must conserve, and that's a problem in open systems. It's contradictory to assess entropy changes in a system which energy is changing.
The third law states that entropy is $0$ when temperature is $0K$. This implies the negation of Einstein's energy-mass equivalence. In fact, here we are saying that entropy is zero (zero energy dispersal) in the whole, the gas container, or the kitchen. We are stating that entropy (whatever it means, which is related to the energy) is zero within a portion of matter. Our subjective, fragile, human-rational perception is tracing the line between mass and energy (and quantum physicists come to the rescue: "wait! there is still ground state energy!!!, so don't say that entropy is zero, say, perhaps that entropy is... a constant!" (which evidently contradicts the essence of the 3rd law)), assuming that energy and mass are completely different physical features. Well, they are not. But we need this false truth in order to use the other two laws.
Finally, the zeroth law (temperature is a transitive relation) just formalizes the feeling that is temperature, in order to be used as a physical fact. Arieh Ben-Naim states that temperature should be expressed in energetic units. I've always considered this as a good idea, but, well, in the meantime we're stucked with Kelvin.
Hope this answers to your question, but of course, sets new questions (that's why the book-memorizing-without-asking-obvious-questions approach is wrong: science has problems; science can only be perfect for fools!). The following link addresses the false truth presented above. In simple terms, the false truth is accepting that our perception is the truth, but that's not correct. Macrostates correspond to our perception, and microstates to that which we cannot perceive. But thermodynamics is not strict with such separation: the microstatic level includes several facts that correspond to our perception; mainly, the existence of things or solid objects (e.g. molecules as objects that have absolutely no internal energy) as physical facts. We know that things are just manifestations of our perception, not real physical facts.
https://philosophy.stackexchange.com/a/57718/23407
