Great explanation, although I want to clarify that not all nebulae are galaxies. Nebulas are massive clouds of dust and gas that are found within galaxies. Other galaxies were previously thought to be nebulas in space outside of the Milky Way, called extragalactic nebulae. However, in the early 1900s it was proven that these were actually other galaxies and not nebulas, so the term is no longer used.
While there are nebulae in other galaxies, they are not easily visible to us, so the word nebula generally refers to those contained within the Milky Way.