The "W" number determines what low ambient temperature the oil is safe to use. Oil has two characteristics: whether it waxes or solidifies when cold, and then how well it flows. Think of sucking on a milkshake - you can **** a hole in a cold one if a) it's really mostly solid, or b) it's so thick that it won't slump into the hole. A 15W-xx is safe down to -20C, a 10W-XX down to -25C, 5W-xx to -30C, etc.
The second number is a single measurement determined at 100C.
A single grade 30, a 5W30, and a 0W30 should all measure between 9.3 to 12.5 cSt at 100C. It does not mean that one of those three is thicker than another at 100C.
Bear with me now. The viscosity at low temperatures and at high temperatures can be plotted on a viscosity (y-axis) vs. temperature (x-axis) graph. The slope of the line is the "viscosity index." A 0W30 will have a flatter slope than a single grade 30. That would mean than at temperatures higher 100C, the 0W30 would be thicker, since it changes less with temperature. Careful - it's not thicker than an SAE 30, because by definition, the viscosity grade is a snapshot at 100C. But when the oil goes over 100C (212F, and oil can easily run in the high 200's) the multigrade will be thinner, but not as thin as the single grade would get.
A thicker oil may (may!!) provide better bearing protection, but at the risk of being too thick for safe starting when cold. Yes, an ideal oil would be a 0W-50, but that strecthes even the synthetic oil formulators. 5W-40 is great all around, 0W40 also.
In the US, OEMs are driven by emissions and fuel economy and almost have to recommend a 5W30. The current fuel economy specifications for engine oils don't even allow grades thicker than a 10W30 to apply for testing.