string someVariable = (string) someOtherVariable;
this is your good old normal casting and it will throw an exception if you try to cast something into something it CANNOT be casted (thus some times you need to check if they are castable)
string someVariable = someOtherVariable.ToString();
is not really casting, its executing a method that may come from different places(interfaces) but that ALL objects in C# have, since they inherit from the Object object, which has it. It has a default operation which is giving the name of the type of the object, but you can overload it to print whatever you want your class to print on the ToString method.
string someVariable = someOtherVariable as string;
This is a new c# casting, it will check first if it is castable by using a variable is string
first and then doing the casting if it is valid or return null if it is not, so it could be a silent error if you are expecting exceptions, since you should check against null.
Basically
myType as myOtherType
is the same as:
var something = null;
if(myType is myOtherType)
{
something = (myType) myotherType;
}
except that as will check and cast in one step, and not in 2.