It's not about " Tighter tolerances " , etc. 0w-20 oil yields a slightly better fuel economy which is critical to conform to CAFE standards .
That will surprise my auto shop owner (for the past 20 years) who told me that. I personally have no direct knowledge of engine tolerances.
Actually it is both.
Multi-viscosity oil is formulated to meet specific viscosity parameters at two specific temperatures - the freezing and boiling point of water.
The 0W20 designation means that at 32*F the oil has the same properties as single-weight 0 viscosity oil. It has the same viscosity/thickness/flow characteristics as 0-weight oil. At 212*F it has the same viscosity/thickness/flow characteristics as 20-weight oil.
Modern engines have tighter tolerances (clearances) between the bearings and rotating parts - like the crankshaft, camshaft, & rod bearings. Those smaller clearances require thinner oil in order for the oil pump to be able to push the oil into the space between the bearings and the rotating parts. It is this pressurized oil that keeps the parts from actually touching and creating metal to metal contact and wearing out the parts.
Since cold oil is harder to pump and more resistant to flow, reduced viscosity at low temperatures makes it easier for it to flow and lubricate the parts when the oil is cold. As oil warms up it gets thinner - lowering viscosity - so it is important for the oil to have a higher viscosity rating at high temperatures so that it maintains its ability to lubricate the parts and prevent the metal to metal contact that wears out parts.
Higher weight, thicker oil creates more drag on the rotating parts and takes more power to turn the oil pump pushing the oil throughout the engine. That drag is a parasitic power loss - some of engine's power is wasted overcoming the drag and pumping resistance. Since that lost power comes from the engine burning fuel, the lost power is wasted fuel.
One other aspect of the resistance to flow is that that pumping resistance itself is a form of friction that adds even more heat to the oil. Simply pumping oil raises its temperature, and the thicker it is the more heat will be created in the oil just from the friction of being pumped through the system.
So thinner oil experiences less of this pumping friction and stays cooler. Heat is one of the things that causes oil molecules to break down, so less heat from pumping friction also helps the oil to last longer without breaking down. That's one of the reasons modern cars have so much longer recommended oil change frequencies. The oil holds up better and lasts longer before it starts to break down from heat.
One really great thing about synthetic oil is that the oil molecules are chemically engineered to all be identical length chains of molecules. "Natural" distilled oil contains a mix of different length molecule chains. So, the synthetic is much more uniform in its composition. You can think of it as tighter quality control.
This tighter quality control and consistency is another one of the main reasons that newer vehicles have much longer recommended oil change intervals. The oil maintains its consistency for much longer without breaking down.
