The International Astronomical Union defined a planet as an object that:
To be a planet, it must orbit OUR SUN. Celestial bodies orbiting other stars are Exoplanets.
I should have capitalized Sun in my post, but honestly, I think the difference you mentioned is encapsulated in the use of a definite article 'the sun' instead of the indefinite 'a sun.'
It is like saying that there are only 69 Cities in the world, which is true... if we're using the UK's letters patent/royal charter definition of a city. I was hoping my comments would be taken as poking fun at the IAU's definition, which as @sumguy pointed out is ridiculously narrow, especially as they have no definition for exoplanets!
Have some ize in your drink?