Viscosity ratings are not exactly straight forward and often cause confusion.
A 10W-30 oil has a cold viscosity equivalent to a cold 10-weight reference oil.
When a 10W-30 oil is hot, it has the viscosity of a hot 30-weight reference oil.
Straight 50, 20w-50, and 0w-50 oils all have the same "hot" viscosity.
Multi-viscosity oils still get thinner as temperature increases; they just thin-out less than a single-viscosity oil. Viscosity index improvers (VIIs) are the compounds added to a base stock/straight-vis oil to give it that ability. VIIs are also generally the least durable part of the oil, so viscosity breakdown tends to happen faster with oils that have a wider gap between the cold and hot viscosity, especially where shearing is an issue like in motorcycle gearboxes. Not really something to worry about in general applications, but it does happen.
Whether the oil is synthetic or not has no bearing on the viscosity rating, but you're probably only going to find really broad spreads offered in synthetic like 0w-50.