Kenmore Power Spray was the model. As stated by Vacuum Salesman, there are two tanks, the bottom one holds the clean water and the top one is for the dirty water. Some models did have the optional Spray Mate to scrub the carpets. An upholstery attachment was also available. It can be used with the pump turned off for wet or dry vacuuming (bags were available for dry use). There was also a Dry Mate PN available for dry pickup, as well as a floor nozzle and other attachments. Yours appears to be brown and beige, which puts it somewhere in the mid 80s. Earlier models were blue and white. In the early 90s it was red and black as the Heavy Duty series, or all black as the lower cost Cleanmore series. At some point it also came in light and dark gray. Two- and one-speed versions were available.
This machine was made by Ryobi/Singer and the Dry Mate looked like the PN from Singer System Canisters of the era. These were popular systems in the day, though I never saw any myself, I always wanted one. I found one with the Power Spray head at a thrift store a year or two ago, but I had no room to get it.
Later these were replaced with an almost turtle shaped carpet cleaner that also was made by Ryobi I believe and had the same attachments.