Below we will discuss the difference between Bissell Powerfresh and Powerfresh Deluxe.
If you are deciding between the Bissell Powerfresh (such as the model 1940, 1940a and 1940w) and Powerfresh Deluxe such as model 1806, the info should be useful to you.

Both of these 2 machines are designed mainly for cleaning hard floors. They are similar but not identical to each other.
The Bissell Powerfresh, such as the model 1940, 1940a and 1940w, is the original basic model.
While the Bissell Powerfresh Deluxe such as the model 1806 is a newer model, it has some new features.
Here are the main differences between them.

Water Tank design.
Their tank design are different. The Powerfresh 1940 models has a removable water tank whereas the Deluxe 1806 has a built in water tank. So, with the Powerfresh, you can remove the tank to fill and empty, while the Deluxe comes with a measuring water cup for filling.
The Deluxe has larger tank capacity which is 19 oz. versus 15 oz. on the Powerfresh.

Scrubbing Brush.
The scrubbing brush design is another big difference between them.
The Powerfresh has a brush on the back of the nozzle, you can flip it down to use it with the mop pad to clean grout, crevice, and sticky messes.
While the Deluxe has a totally different, redesigned spot scrubbing brush which is located on the bottom, but above the nozzle, when cleaning tough spots, you detach the nozzle to expose this SpotBoost brush, then use the machine with this brush (without the mopping pad) to scrub the touch spots.

Steam Levels.
The Powerfresh has 3 steam levels (low, medium, high) while the Deluxe has 2 levels (high, low).

Scent Disc Holder design.
The Powerfresh has a pocket inside the mop pad, you can insert the scent disc into that pocket while the Deluxe has a separate scent disc holder on the front of the nozzle.

Cord Length.
The Powerfresh has a cord length of 23 feet versus 25 feet on the Deluxe.

Both of them have swivel feature, backed by a 2 year limited warranty, and they have optional carpet glider attachment to enable them to work as a carpet refresher/deodorizer.