I am pretty certain that there is a grammar rule that would make this much easier to understand, unfortunately I don't know this one and have to rely on my gut with this one:
Gemeinsam has the connotation of people doing something together. Not just physically being present at the same time at the same place but really working with each other.
Zusammen does mean the same. People can do something "zusammen" too, which means that they choose not to do this individually but in the presence of one another. They may or may not work together. (If in university we agree to do a presentation "zusammen" this means we'll meat once, everyone does his part and we will hold the presentation together. It basically means we are a group, not necessarily that we really do this together. So that "in the presence of one another" is more a connotation thing than somethings that is really implied.)
If you use it in conection with people those things are interchangeable and I don't think that people will interpret much into which one you choose.
There is a difference when you use it in relations to things, though.
Storys can have something "gemeinsam" which means that they share a theme, a plot or something of the like. If they have something "zusammen", than that's colloquial and they are making out, which - given that they are stories - means it's nonsense.
In this way you can compare things, basically using the German Noun "
Gemeinsamkeit(en)"
But you can put things away "zusammen", meaning that you placed them both in the same drawer or something like that. If you put
a tablecloth "zusammen" however, you are folding it up.
(Ich habe die Tischdecke zusammen gelegt. = I folded the tablecloth up.)
(Ich habe das Geschirr zusammen gestelt. = I pilled up the dishes.)
And if you put things away "gemeinsam", it means that you did it with someone else.
(Wir haben gemeinsam den Tisch gedeckt. = We layed the table together.)
Or you are just really fond of the object you are speaking about. People would look puzzled for a moment were you to say "Ich habe sie gemeinsam weggestellt."
(I have put them away together.)
But if you talk about fotos of greatgrandparents or something or other objects that you think shouldn't be seperated, it would be okay, even if this use is mainly uncommon...
I hope this isn't too confusing.
Sorry, I really can't phrase this any better.
But I hope the basic idea gets through.
Gemeinsam leans more to "to have in common" and zusammen leans more to "together" though they are often used as one and the same.
Does that make any sense?
