The below section is a question originally raised on Quora:
Classical music is referring to the era of time and the art often reflects the time that it was created in and what was going on politically. For example, the piano-forte was invented in the late classical/early romantic era giving way to a larger dynamic range (larger volume shifts) because the new instrument allowed it.
That being said the Baroque era is characterized 1600 to 1750, the classical was considered 1730 - 1820. See the overlap? Inevitably there are going to be similarities. Perhaps the conditions for performance were different. If memory serves me, I think of the Baroque era as being influenced much more profoundly by the church, while the Classical had more of a private funding for concerts unassociated with Church.
Certain composers such as Mozart and Beethoven definitely have elements of classical music, but they were most likely influenced by Bach and other Baroque composers. Especially Mozart who I believe had some direct relationship with Bach.
TL:DR - The art, the politics, and the materials available at the time all had a direct impact on the characteristic sounds found in each type of music.
About Eric -
Eric is a licensed Simply Music Piano Instructor offering mobile piano lessons in the Orange County Area.