Per www.dictionary.com
Drawing room - A formal reception room, especially in an apartment or private house. A shortened version of the now obsolete term "withdrawing room."
Parlor - (Older usage) A room for the reception and entertainment of visitors to one's home; living room.
You know how some houses have a formal living room and also have a den that they actually hang out in? The living room is the drawing room while the den is like the parlor.
Rich people had drawing rooms and morning rooms and dining rooms, ordinary people had a scullery and parlour (sitting room for best ) if they were lucky.
I should have picked your answer for best answer, as I like your analogy better . :)
i have always thought that they were one and the same, being the only difference is that what part of the country the house was located in. Or what country, period.
