What terminologies and concepts describe the codes that follow a format of Text1.Text2()?
The over-arching concept is Object Oriented Programming (OOP).
The terms I was taught at University - taking Serial.println() as an example:

Serial is an instance of a class (in this case HardwareSerial), sometimes called an object.
println() (a function in a class) is a method of a class.
A &quot;variable&quot; in a class is called a property of a class.

A commented code example:

class Foo { // This is the *class*

    public: // These symbols are accessible from outside the class

        int bar; // This is a public property

        void baz() { ​// This is a public method
        }

    private: // These symbols are only available from inside the class

       ​int meep; // This is a private property

       ​void moop() { // this is a private method
       }
};


Foo bar; // Instantiate an instance of the Foo class and call it bar.