One of the main differences between the two is where they come from. Cheongsam is the English version of Cheungsaam. If you are not familiar with this, this term stands for a long dress.
The Cantonese version of Cheongsam is the type of language that is still being used in some parts of China, particularly the Southern area of China.
Qipao is another language that is being used in China, but this is more commonly used in the Northern area of China. You will know from where a Chinese person has come from based on the type of language that they will use, especially if you are familiar with both.