It depends on the clone method implementation.
There are two types of making a copy - deep and shalow.
First of all all value type memebers get their own copy, so changing such a
property or field in one of the objects doesn't affect the other.
Reference types are more interesting. If the clone method is implemented as
shallow copy that means only the reference is copied over the new object.,
thus both, the orginal and the clone, reference the same object in the heap.
In this case changes made via properties of one objects will be reflected by
the other. We have deep copy when not only the reference is copied, but the
whole refernced object is cloned - we have different object in the heap. In
this case all the changes are local for the objects.
As you can see it depends how the clone is implemented.
The object class provides MemberwiseClone method that does shalow copy. Also
when you assign one value type to another you get a shalow copy.