Bear in mind that there are other factors involved, such as sidewall and carcass stiffness, tire reinforcement, and cord orientation and construction.
Softer sidewall and carcass construction can allow a greater contact patch at the same inflation. Tire compound, the numbers and types of plies, and orientation of reinforcements all affect carcass and sidewall stiffness.
Stiffer reinforcement materials, such as steel and nylon cords, can keep a tire more round and subsequently reduce contact at the same inflation than polyester or other textile cords.
Purely radially wrapped cords tend to allow more sidewall flex than crossed/angular orientation (biased) of reinforcement cords of the same material.
Regarding overall traction, there are a lot of factors affecting that. Tread design, inflation, pavement type, condition, and temperature all affect friction coefficients and ultimate traction.
For example, a typical highway tire might have complete circumferential channels and grooves intended to allow water to be displaced and the remaining tread blocks to make better contact. The resultant contact patch is thus reduced by these void areas. A racing slick has no such channels and has a 100% contact area under the patch footprint. They are commonly designed with much softer rubber compounds, less rigid sidewall and carcass construction, and are inflated to 10-12 PSI to maximize the contact area. They also fail miserably for overall traction on anything but warm, dry pavement. Adding some grooves and channels allows some improvement on wet surfaces but maintains good dry traction.
Conversely, a more heavily lugged tire tends to have more and larger void areas and rigid construction. That concentrates more contact pressure over a smaller area. They tend to have a lot lower overall traction on dry pavement, but excel on rain, snow, slush, mud, sand, and dirt.
Somewhere between those is the array of highway tires more commonly used on powered grocery carts, better represented by your passenger car tire chart above.