No those two terms do not synonym . It is just that those two terms are related to each other because of the bollywood industry is in mumbai. It is done so as to fun.
Bollywood is not like Hollywood. Bollywood is not even a place. Its just a name for all Indian movies and music. Although Mumbai in India is the movie making capital of the world. But Bollywood is indeed not a place!
BollywoodIt is, in the words of Humpty Dumpty, a 'portmanteau' word. It was created by merging Bombay with Hollywood, indicating the merge of India with the entertainment world.
Bollywood
Mumbai Mumbai
The headquarters of Bollywood are in Mumbai. It is the home to all the actors. The complete film industry is located there.
Bollywood originated from Bombay (now Mumbai), India.
Mumbai music usually refers to Bollywood music. Bollywood is the second largest film industry in the world after Hollywood.
Bollywood is located in the heart of india-in other words in Bombay(Mumbai).
They all have one thing in common. The common thing is the MUMBAI city. Bombay is the old name of Mumbai and Bollywood is there in Mumbai.
Bollywood is in the continent of Asia the country of India and the city of Mumbai.
Mumbai
Bollywood is the Indian equivalent of Hollywood.