length() is an instance method of the String class, so you call it on a specific instance (object) of type String. For example: name.length().
On the other hand, sqrt(...) is a static method of the Math class. There isn't any particular Math object that you're working with -- so you just call it by putting the class name (Math) in front of it.
Similarly, when we create our own methods inside a program, so far we have always made *static* methods, which belong to the program/class as a whole. They aren't attached to a specific object. For instance, the gangstaName method we wrote was a static method. We passed in the String name as a parameter -- gangstaName(s) -- we did NOT call it like: s.gangstaName(), which we would have done if gangstaName was an instance method inside of the String class.
Some other examples of instance methods include drawOval for Graphics objects, nextLine for Scanner objects, getGraphics for DrawingPanel objects, etc.
Hope that helps...