The differences in the different types of motor oil for automobiles. 10W40; 0W20; etc.

My old car uses a 10W40, and my wife's new SUV uses a 0W20.  The sticker put on the windshield for both suggests changing every 3,000 miles.  Is this a sales ploy or does oil still need changing so soon?  What are differences in the different types of motor oil?
There are three different types of motor oil for automobiles: conventional, synthetic, and a mix of the two [1]. Conventional motor oil is the type of motor oil that has been used for decades and can be found at most gas stations [1]. Synthetic motor oil is a newer type of motor oil that began to be used in the late 1990s [1]. There are advantages to using synthetic motor oil, such as it being lighter and having a higher temperature tolerance than conventional motor oil [1]. However, synthetic motor oil is also more expensive than conventional motor oil [1]. Mixing the two types of motor oil, conventional and synthetic, creates a third motor oil that is a compromise between the two types [1]. The differences between these different types of motor oil will determine how it performs in your car [1].
There are many different types of motor oil because of the different temperatures they need to operate at [1, 5]. The numbers you find on different oil cans, such as SAE 30 or SAE 10W-30, are viscosity or weight numbers that indicate the thickness of the oil [2, 3]. The higher the number, the thicker is the oil [2, 3]. As earlier mentioned, SAE stands for Society of Automotive Engineers [3]. An additive package comprising polymers is blended into the oil. Polymers expand when heated, so the oil actually maintains its viscosity to the point where it is equal to what a hot SAE 30 oil would be [4]. This ability to resist change in viscosity as the oil heats up is referred to as viscosity index [4]. Motor oils also include additives to reduce changes in viscosity because of temperature [5]. Certain motor oils are designed to be thinner (less viscous) when cold and more viscous (thicker) when hot [5]. The idea is to provide thin oil when the motor is started and to provide an oil of the right thickness at the operating temperature [5].