57-622 tyre confusion

There are different way to define the size of tires, which is confusing.

57-622 refers to a tire with a width of 57mm, that fits in a rim with a bead seat of 622mm.

The difference between 700x35C and 700x40C is the width of the tire (the second number being the width expressed in mm) ...but that kind of denomination is not correct strictly speaking. In the French nomenclature, the first number is the diameter of the wheel, tire included. It is then followed by a letter: A, B, C, D, that represented the height of the tire. It should be 700C or 700B, but some people have forgotten that and seem to consider that 700C = 622mm.

622mm bead seat is probably the most common size nowadays, used by 29in MTBs, road, gravel (although some have smaller wheels), city bikes,... Some marketers also had the brillant idea to invent a new name for "thin 622mm": 28in (size in inches also refer to the external diameter of the wheel). As pointed earlier, with a 29in, you have quite a range of choices for your tires, provided that they are suited to the inside width of the rim. Wide gravel tires can also be a good compromise if you want to keep some offroad cabilities.

Also keep in mind that inner tubes must also be properly sized. They usually support different widths (the ones on my bike go from 35 to 47mm for example). So if you want to go from 57mm to 40mm, you may have to change them as well.

For reference, rolling resistance is also linked to adherence. Depending on what you do with your bike, taking tires like the ones you showed might seriously impact the capabilities of your bike on loose surfaces. Most tires manufactures have charts recommend what tires could be more suited for the surfaces you intend to ride on (the Smart Sam represent for me the best compromise if you mix often trail and road, that being said).