Let's take your example of a Dog and a Cat class, and let's illustrate using C#:

Both a dog and a cat are animals, specifically, quadruped mammals (animals are waaay too general). Let us assume that you have an abstract class Mammal, for both of them:

public abstract class Mammal

This base class will probably have default methods such as:

• Feed
• Mate

All of which are behavior that have more or less the same implementation between either species. To define this you will have:

public class Dog : Mammal
public class Cat : Mammal

Now let's suppose there are other mammals, which we will usually see in a zoo:

public class Giraffe : Mammal
public class Rhinoceros : Mammal
public class Hippopotamus : Mammal

This will still be valid because at the core of the functionality Feed() and Mate() will still be the same.

However, giraffes, rhinoceros, and hippos are not exactly animals that you can make pets out of. That's where an interface will be useful:

public interface IPettable
{
    IList<Trick> Tricks{get; set;}
    void Bathe();
    void Train(Trick t);
}

The implementation for the above contract will not be the same between a cat and dog; putting their implementations in an abstract class to inherit will be a bad idea.

Your Dog and Cat definitions should now look like:

public class Dog : Mammal, IPettable
public class Cat : Mammal, IPettable

Theoretically you can override them from a higher base class, but essentially an interface allows you to add on only the things you need into a class without the need for inheritance.

Consequently, because you can usually only inherit from one abstract class (in most statically typed OO languages that is... exceptions include C++) but be able to implement multiple interfaces, it allows you to construct objects in a strictly as required basis.

Short Answer

Use $this to refer to the current object. Use self to refer to the current class. In other words, use $this->member for non-static members, use self::$member for static members.

Full Answer

Here is an example of correct usage of $this and self for non-static and static member variables:

<?php
class X {
    private $non_static_member = 1;
    private static $static_member = 2;

    function __construct() {
        echo $this->non_static_member . ' '
           . self::$static_member;
    }
}

new X();
?>

Here is an example of incorrect usage of $this and self for non-static and static member variables:

<?php
class X {
    private $non_static_member = 1;
    private static $static_member = 2;

    function __construct() {
        echo self::$non_static_member . ' '
           . $this->static_member;
    }
}

new X();
?>

Here is an example of polymorphism with $this for member functions:

<?php
class X {
    function foo() {
        echo 'X::foo()';
    }

    function bar() {
        $this->foo();
    }
}

class Y extends X {
    function foo() {
        echo 'Y::foo()';
    }
}

$x = new Y();
$x->bar();
?>

Here is an example of suppressing polymorphic behaviour by using self for member functions:

<?php
class X {
    function foo() {
        echo 'X::foo()';
    }

    function bar() {
        self::foo();
    }
}

class Y extends X {
    function foo() {
        echo 'Y::foo()';
    }
}

$x = new Y();
$x->bar();
?>

The idea is that $this->foo() calls the foo() member function of whatever is the exact type of the current object. If the object is of type X, it thus calls X::foo(). If the object is of type Y, it calls Y::foo(). But with self::foo(), X::foo() is always called.

From http://www.phpbuilder.com/board/showthread.php?t=10354489:

By http://board.phpbuilder.com/member.php?145249-laserlight