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In movies and TV to save on royalties they would play a song that almost sounds like another popular song with just a few notes changed. They are meant to fool the audience or at least try to give off the same effect.
Example: Escape montage from Take the Money and Run sounds like Quincy Jones' Soul Bossa Nova.
Original :
Marvin Hamlisch's imitation:
What are those types of songs called?
It's called a Pastiche
A pastiche is a style of music [or art] that imitates the style or character of a piece. Unlike a parody, it celebrates rather than mocks the original.
Adverts and 'high number' cable channels keep hordes of composers in business by employing their skills at this 'style copying' rather than paying for the original music.
After further thought - though the technical musical term is pastiche, very often in a brief for music, production will simply call it a Sound-alike [presumably because they're not themselves musicians.]
The term for a piece of music that imitates a specific other piece of music is a soundalike. They are generally disliked in the industry because they are considered a cheap attempt to profit off an artist's creativity and hard work without providing him or her any of the profits or benefits --the concept is basically the same as a knockoff item of clothing in the world of fashion.
(Note: while this is a part of Tetsujin's answer, I'm posting it separately, because I disagree with the other portion of his answer).
