Oxygenated gasoline, unlike regular gasoline, has had compounds added to it. These compounds are called alcohols or ethers and they contain oxygen in their chemical formula. For example, methanol is an alcohol and its chemical formula, CH₃OH, contains an O, which stands for oxygen. By adding chemical compounds that contain oxygen to gasoline, you can increase the ratio of oxygen-to-fuel in a car engine.

The engine is a pretty well-contained system, so it's difficult to get good airflow. Poor airflow or lack of oxygen leads to incomplete combustion of fuel. Normally, when we think of burning fuel, we assume that fire or an engine takes in fuel and oxygen and releases heat, carbon dioxide, and water. However, this is only when it burns the fuel completely! When it doesn't have enough air, the engine will still create water, but instead of carbon dioxide you'll get carbon monoxide and carbon in the form of soot.

Both carbon dioxide (CO₂CO₂) and carbon monoxide (COCO) are considered greenhouse gases, but we prefer our fuel to release CO₂. That's because when we inhale CO, it binds so tightly to hemoglobin in our blood that the hemoglobin cannot pick up oxygen and leads to headache, dizziness, and vomiting at low levels of carbon monoxide poisoning and death at large exposures.

Getting down to differences between oxygenated fuels, in September 1998, the California Air Resources Board published An Overview of the Use of Oxygenates in Gasoline where they noted that depending on what oxygenate was used, evaporative hydrocarbon emissions may change. Essentially, this meant that the liquid fuel itself would vaporize into the air as one type of fuel emission. Oxygenates that make the gasoline vaporize more easily—like ethanol—can increase both hydrocarbon and ozone-forming compound emissions.[1]

According to this more recent 2019 study on vehicles in Korea, as the oxygenates ethanol (EA), methyl tertiary-butyl ether (MTBE), and ethyl tertiary butyl ether (ETBE) percentage in gasoline increased, the CO, non-methane hydrocarbons (NMHC), and nitrogen oxides (NOx) emissions decreased. MTBE-oxygenated gas emitted more CO than EA- and ETBE-oxygenated. EA was best at reducing CO emissions, followed by ETBE, then MTBE. All three oxygenates released similar concentrations of NMHC in their fuel emissions.[2]

References:
[1] Gomez, Jose, et al. California Environmental Protection Agency, 1998, An Overview of the Use of Oxygenates in Gasoline , ww3.arb.ca.gov/fuels/gasoline/pub/oxyrprt.pdf. ↩︎
[2] Lim, Cheol-Soo, et al. “Comparative Effects of Oxygenates-Gasoline Blended Fuels on the Exhaust Emissions in Gasoline-Powered Vehicles.” Journal of Environmental Management , Academic Press, 18 Mar. 2019, www.sciencedirect.com/science/article/pii/S030147971930341X . ↩︎

Oxygenated gasoline contains an additive derived from natural gas or grain alcohol that increases the fuel's oxygen content, causing more complete combustion in the engine and reducing emissions of toxic carbon monoxide.

People were complaining about getting sick from it, but the State Department of Environmental Protection and Energy noted that carbon monoxide emissions were reduced 14.9 percent last winter, as a result of motorists' using oxygenated gasoline.

Oxygenates are fuel additives that contain oxygen, usually in the form of alcohol or ether. Oxygenates can enhance fuel combustion and thereby reduce exhaust emissions. Some oxygenates also boost gasoline octane. The Clean Air Act requires use of oxygenated gasoline in areas where winter time carbon monoxide levels exceed federal air quality standards. Without oxygenated gasoline, carbon monoxide emissions from gasoline-fueled vehicles tend to increase in cold weather. Winter oxygenated gasoline programs are implemented by the states.
Source.

1. From the US National Academy of Sciences - chapter 2 of a book.

2. This one has info from 2019.

I am not sure, but I would predict that there would be fewer hydrocarbon byproducts of combustion.

In general, the smaller the gasoline molecule, the more cleanly it burns.

A complete combustion equation for methane looks like this:
CH₄ + 2O₂ --> CO₂ + 2H₂O.

However when burning a solid like wood, for example, carbon particulates and carbon monoxide are also formed as byproducts in addition to the carbon dioxide and water vapor. Byproducts form in local areas around the fuel that are more oxygen deficient. It is impossible to get perfectly clean combustion, but the higher the surface area to volume ratio of the fuel, the more cleanly it burns. This applies on the macro scale (pellet stove fuel burns more cleanly than firewood) and also on the molecular scale:
typically methane will burn more cleanly than a larger molecule like octane.

The examples I gave were all for fuels that are hydrogenated carbon chains at the molecular level. I'm not familiar with more oxygenated gasolines, but perhaps some of the same rules apply.