Let me try to explain again and perhaps clear up the confusion if I can.
As has been pointed out, there are three types of systems usually defined in chemistry, for instance in Barrow which I also used as an undergrad way back when and as quoted by DNAunion on the previous page with more detail.
Open: exhanges matter and energy with the environment
Closed: exchanges energy but not matter
Isolated: exchanges nothing
The confusion arises because when engineers or physicists refer to a closed system they often mean a system that is
adiabatically closed. This means that no heat flows in or out of the system, thus an adiabatically closed system is an
isolated system. Sometimes isolated systems are alternatively referred to as closed systems with athermal boundaries which means the same thing. Badfish in the original post specifically referred to an adiabatically closed system at one point but then wrote
Entropy (disorder) always increases or remains constant in a closed system.
This statement is
only correct because he said he was talking about an adiabatically closed system in the preceding paragraph. Read without this qualifier the statement is not correct. I assume that this is the source of the misunderstanding. I thought badfish was wrong when I saw the statement at a first glance but then I saw that he said adiabatically closed so the statment is correct since it is obvious that he meant the adibatically closed system he had just referred to above.
I prefer the terminology, open, closed and isolated but sometimes physicists mean adiabatically closed, or isolated when they simply say closed.
I don't want to seem to be arguing from my own authority but I have spent quite a bit of time studying, working with, and occasionally teaching thermo over the years. The interesting thing is that if I read either lucaspa's or DNAunion's posts in isolation (pun intended) I don't see that either of them is formally wrong. Lucaspa is right that for closed systems as defined in physical chemistry and even in a quote that DNAunion posted, you must consider the system and the surroundings and that the system and the surroundings make the isolated system, however DNAunion is right that closed systems that are adiabatically closed which is what he means by closed(isolated) do not interact with their surroundings and that for such systems entropy is constant or must increase. They almost seem to be making a deliberate effort to misunderstand each other here.
A note to DNAunion: When you write closed(isolated) system as you have , I think you may be adding to the confusion a bit. I know what you mean but not everyone may. If you are going to call a closed system isolated you should specify that it is adiabatically closed especially when you give the standard definition of a closed system, that is not isolated in a subsequent post.
In any case, as I pointed out it doesn't matter to evolution since the earth is not an isolated system. I don't think it matters to the big bang either even though the expansion of the universe is thought to be adiabatic, since the microwave background is a source tremendous entropy because it is a huge amount of very diffuse energy.
Hope this helps. Maybe I wasn't too clear the first time. (Maybe not this time either but that's about the best I can do.)
The slightly frazzled Frumious Bandersnatch