Why in the class declaration does it change the firstMessage object. Are they the same objects?
The example you gave is a really nice one because it succinctly illustrates the difference between class and struct, and you came about this close -> <- to answering your own question, even if you didn't realize it. As the other answers have explained, class creates a reference type, which means that when you assign an instance of a class to a variable, that variable gets a reference to the object, not a copy of it. You said so yourself:
//if I assign, its a reference to the original instance
var secondMessage = firstMessage
In your example, firstMessage and secondMessage are really references to the one object that you created. This kind of thing is done all the time in object oriented languages because it's often important to know that you're dealing with a specific object and not a copy, especially if you might want to make changes to that object. But that also brings danger: if your code can get a reference to an object and change it, so can some other code in the program. Shared objects that can be changed create all kinds of headaches when you start writing multithreaded code. When you added text to secondMessage, firstMessage also changed because both variables refer to the same object.
Changing the declaration of Message to struct makes it a value type, where assignment (for example) creates a new copy of the object in question instead of a new reference to the same object. When you added text to secondMessage after changing Message to a struct, the assignment secondMessage = firstMessage created a copy of firstMessage, and you only changed that copy.
Is this a rule that if I assign a new object from the old object?
Whether your assignment creates a copy of the object or a reference to it depends, as you've shown, on whether the thing being assigned has reference semantics (class) or value semantics (struct). So you need to be aware of the difference, but most of the time you don't need to think too hard about it. If you're dealing with an object where you don't care about the object's identity and are mainly concerned with its contents (like a number, string, or array), expect that to be a struct. If you care about which object you're dealing with, like the front window or the current document, that'll be a class.
Then I would have to declare secondMessage = Message() to make it a new instance.
Right -- if Message is a class, assigning one to a new variable or passing it into a method won't create a new one. So again, are you more likely to care about which message you're dealing with, or what is in the message?