Motor oil (which I actually prefer to call Engine Oil, since your car's source of motive power is more properly called an engine) is a confusing subject for many. Is there really a difference one to another?
Yes, there is-- and some differences matter, while others matter very little.
The single most important variable in an engine oil is viscosity, or how thick it is. This is the thing you should care about the most, and most people could pay attention to only this factor and be just fine with any national brand.
Related to the differences in oil thickness are how that oil changes thickness across temperatures. We all know that "molasses in January" is rather thick, but hot cooking oil can be almost water-like in consistency.
What a lot of people don't realize is just how non-linear is this behavior is. Notice on this graph that once you get the oil up to it's normal temperature (about 100C, the boiling point of water), the difference in thickness are too small to see on this Y-axis scale. You'd need to re-scale the graph to even note the difference.
The basic idea: cold oil is bad oil. The engine is designed to oil be a certain thickness (about 8-12 cSt), and any oil is too thick at even room temperature. Let's zoom in a little bit:
The chart above chose that even the thinnest oil (5w-30 here) on a sweltering hot day (40 degrees C is 104F) is still about SEVEN TIMES TOO THICK when the engine is "cold" on that sweltering summer day. So, if a "thin" oil on a hot summer day is 7x too thick, then you can be very comfortable assuming that a thick oil (like a 15w-40) is far worse on a cold day. For example, the first chart shows a 15w-40 oil on a cold winter start (32F) to be about 130x too thick! Now, this is at 32F, never mind what you frozen Midwesterners mights see on a -40F winter morning.
It's clear that the change in oil thickness with oil temperature is a bad thing. It turns out that some oils change thickness much less than others, even within the same "rating."
While all oils thicken as they cool, some thicken much less. Generally, synthetic oils excel in this regard.
Generally, the further apart are the numbers on the bottle, the less the oil thickens. There is a point where an oil gets so thick that it won't pour and it's essentially frozen solid. The colder that temperature, the thinner the oil is at temps warmer than that (and that's a good thing). For example, Rotella 15w-40 has a pour point of -30C, but Mobil 1 0w-30 is all the way down to -50C.
What about the resistance to heat? For most people, this isn't much of a factor. Oil temperatures in a properly running engine rarely, if ever, enter the danger zone. Not even in Death Valley in August. Most automotive cooling systems are sized to be able to let the air conditioning function in extreme heat. By comparison, keeping the engine oil cool is much easier and your oil holds a pretty steady temperature even on the hottest days.
The only real advantage of thicker oil is at extremely high oil temperatures that are a almost never going to happen in a modern, liquid-cooled car.
Next time you buy oil, just buy the thinnest stuff you can find in a nationally known brand (Valvoline, Mobil, Castrol, Havoline, Pennzoil, Quaker State, etc). If you do lots of cold starts in a climate that gets cold winters, buy the thinnest synthetic oil (mobil 1, Castrol Syntech, Royal Purple, etc) you can find.
Change the oil every 200 gallons of fuel you burn (for most cars that hold ~ 5 quarts) and don't worry about it anymore than that.