I currently have Smart Sam Active Line K-Guard 29" tyres on my bike with a profile of 57-622. I'm trying to source replacements, ideally ones with less rolling resistance. I have found these but I'm confused by the sizing. Would 700x40C or 700x35c fit and if so, what's the difference between the 40 and 35?
622mm ISO bead seat diameter is referred to as sometimes 700. So 700x40C and 700x35C are 622-40 and 622-35 using less confusing terminology.
To see if 622-40 or 622-35 fits, you need to measure your rim inner width. If the rim is a hook-type rim (very likely), then add a millimeter to the caliper reading. Then look at this table to see if the 622-40 and 622-35 tires fit.
The narrowest rim for which 622-57 is recommended is 622-25C, and the narrowest recommended tire for 622-25C rim is 622-44. However, sometimes bike manufacturers use excessively narrow rims such as 622-23C which officially only accepts tires up to 622-50 so 622-57 is already a non-recommended tire.
If your rim is 622-23C (or narrower) then 622-40 tire will fit. If your rim is 622-21C (or narrower) then 622-35 tire will fit too.
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).