Which method
actually works?

Hot water extraction removes deep soil and is the method the Carpet and Rug Institute and most major carpet manufacturers publish. Dry methods clean the surface and dry faster, which makes them useful for interim commercial maintenance but not for restorative cleaning.

No, and the gap is mostly heat and vacuum. A truck-mounted unit produces water temperature and airflow no portable can approach, and vacuum determines whether soil leaves the building or settles back into the fiber as it dries.

Steam cleaning in ordinary use means hot water extraction. Shampooing uses a foaming detergent worked into the pile and is largely obsolete because rinsing it out completely is difficult.

Different cycles rather than different totals. Carpet is vacuumed often and extracted on a schedule, and it hides its soil until the traffic lanes go grey. Hard floor is swept constantly and shows every crumb, and it hides its wear instead — the grout darkens and the finish dulls a little at a time under the same grit.

You can improve grout by hand, but you cannot reach what is inside it. Grout is porous, and a mop pushes dirty water into it. Pressure plus simultaneous extraction is a different physical process from anything achievable with a brush.