It would only be the same if we felt that many of the descriptions could apply to us. For example, the ESFJ doesn't seem like you :)
'ESFJs are people persons - they love people. They are warmly interested in others. They use their Sensing and Judging characteristics to gather specific, detailed information about others, and turn this information into supportive judgments. They want to like people, and have a special skill at bringing out the best in others. They are extremely good at reading others, and understanding their point of view. The ESFJ's strong desire to be liked and for everything to be pleasant makes them highly supportive of others. People like to be around ESFJs, because the ESFJ has a special gift of invariably making people feel good about themselves.'
The Forer effect doesn't necessarily require that everyone feels that a specific characterization applies to them: only that the person being characterized feels that that specific characterization applies to him. This is an important difference, because it allows astrologers, illusionists and their ilk to use all kinds of the usual psychological insights to determine broadly into which category someone falls, before coming up with a characterization that will necessarily be recognizable to someone in that category.
Anyone can put me in the INTJ, ENTP or the two intermediate categories. That's already 4 out of 16. Now collect some characteristics from those 4 and mingle: voila, you have produced something I will consider recognizable. In this way, everyone is as good a psychologist as Jung.
'ESFJs are people persons - they love people. They are warmly interested in others. They use their Sensing and Judging characteristics to gather specific, detailed information about others, and turn this information into supportive judgments. They want to like people, and have a special skill at bringing out the best in others. They are extremely good at reading others, and understanding their point of view. The ESFJ's strong desire to be liked and for everything to be pleasant makes them highly supportive of others. People like to be around ESFJs, because the ESFJ has a special gift of invariably making people feel good about themselves.'