[TPIN] Brass Instrument vs. Mouthpiece amplifier

[Aquilo]

Hello,

     I am a trumpet player in highschool, and I am very interested in the
physics and mechanical workings of brass instruments.  Recently I have been
thinking alot about how my trumpet works, and how it differs from my
euphonium (which is a secondary instrument of mine.)  Most questions I have
had were easy to answer, but no matter how hard I look, I cannot find the
answer to one question:

What makes a mouthpiece amplifier into a trumpet/bugle/brass instrument?

Let me explain:
     I realize that all brass instruments are essentially only amplifying
and modifying the original buzz of the mouthpiece.  However, when I put my
mouth piece in a tube, it plays out the other end the same pitch I buzz into
it.  When I place my mouthpiece in my trumpet, I can buzz a tone and it will
play the closest pitch to my buzz in the harmonic series of my instrument
(even if severely out of tune.)  What I want to know is what makes this
difference?

Thank you to anyone who can explain this, as it has plagued me for a while
now.
Thank you very much,
Matthew Cox