If melacha means work, schlepping the soda should be forbidden, and turning on the TV permitted. The answer is that melacha does not mean work. There is no one word. Melacha is a concept related to the act of creating. So too the word tamei.
Many people mistranslate tamei, saying it means impure or contaminated.
The truth is that tamei, similar to melacha, is a concept. This concept is a vacuum of life. Similarly, when a woman gives birth, although she is doing the most beautiful act known to humanity, bringing life into the world, in regard to her own physical body there is a vacuum of the life she had been carrying inside her. Unfortunately, there is a misconception that the Torah is anti-woman. Men and women are equally important before G-d.