Is my understanding of down / upcasting correct?

//creating new object called treet of type Treet
Treet treet = new Treet("Craig Dennis", "Example text", new Date());

//This is Upcasting yes.
//Because Object is a superclass for Treet so we could assign it to another variable like below.
Object obj = treet;

//This is Downcasting. 
//It sais to compiler to treat the obj Object as a Treet Object so you more specified
Treet another = (Treet) obj; 

Object obj = treet;
Treet treet = new Treet("Craig Dennis", "Example text", new Date());

//Because of the type chain treet have all the methods both Treet and Object types have
//So both statements below are correct
treet.getName(); //this is an Treet method
treet.equals( anotherTreet ); //this is a Object method

//But if you would use the obj variable instead one of the two would generate an error
obj.getName(); //this is incorrect because Object type does not have a getName() method;
obj.equals( anotherTreet ); //this is correct because is obj is Object type

//but if we cast the obj variable as a treet we can use both methods again
Treet another = (Treet) obj; 
another.getName(); //correct
another.equals( anotherTreet ); //correct

//This is a part of o chat that sends Strings from a Client to a Servers. 
//I will not give many details but what is important

Object obj = socket.readObject();

//I know that the client send a String variable but I have to save it as a Object first now because 
//the readObject() method returns an object. To utilize it as a String i have to downcast it like below:

String message = (String) obj;
System.out.println(message);