Hot water extraction or steam cleaning uses hot water applied to carpet fibers with a high-pressure wand. The hot water and pressure both work to dissolve thick dirt, mud, dust, and other debris from carpeting, allowing it to be extracted easily.

I'd shampoo if you want them clean, as it uses detergent and water and then the machine extracts the dirty water. Steam cleaners often just shoot steam at things with no way of lifting the dirt off (unless you wipe it away) which isn't great on carpets. It will sanitise, but not clean.