What are the differences between fuel types (comparing with vehicles)?
Broadly speaking, there are three families of motor fuel that you're probably interested in: Diesels, Kerosenes, and Gasolines.
The difference between the families mainly has to do with the molecular weight (and thus boiling point / vapor pressure) of the fuel components - in order above from heaviest to lightest. The differences within each family are related to refining, blending, and additives, as well as process controls imposed on the fuel.



The Diesel Family

In the diesel family we have things like Highway Diesel and the various grades of home heating oil.  

For transportation purposes these fuels are used in compression-ignition engines ("diesel engines"), where a high temperature and pressure will cause the fuel to ignite and burn, producing power.
For other purposes (like heating) we basically light the stuff on fire and are happy it burns.

The Kerosene Family

The Kerosene family are close cousins of the Diesels, including K-1 and K-2 Kerosene (obviously) and Jet-A.

Jet-A is a high-purity kerosene based fuel manufactured under a specific ASTM standard (D1655), with specific physical properties, and is used in jet turbine engines.  Fuel not meeting the Jet-A specification is generally recycled in the production chain for other purposes (for example it may be used in blending kerosene for heating, or blended into highway diesel).

Jet-A is suited for turbine engines, but can also be burned in other compression-ignition piston engines like diesel can (there are a wide variety of aerodiesel engines available from several manufacturers).

Other grades of Kerosene are used for motor fuels, cooking fuel ("camp stove fuel" is typically kerosene) heating, lighting, etc. depending on their refining and purity.

The Gasoline Family

In the gasoline family we have Avgas, Autogas, and "Gasohol", all designed for use in spark-ignition engines.

Aviation Gasoline (Avgas)

Avgas actually comes in several grades, all manufactured to an ASTM standard (D910), with specific physical properties and specific permitted and required additives (such as Tetra-Ethyl Lead - TEL).   

The grade (octane rating) of aviation gasoline is identified by colored dyes added to the blend.
The colors used in the US are:


Green: AvGas 100 (100/130 Octane)
Blue: AvGas 100LL (100/130 Octane)
(This was formulated as a replacement for AvGas 100, with half the lead - hence 100LL - Low Lead)
Red: AvGas 80 (80/87 Octane)


Generally 100LL is the most widely available aviation fuel because it works in the widest range of engines. 

Autogas (automotive gasoline)

Automotive gasoline comes in multiple octane grades, but generally it's all varying blends of "regular" (87 octane) and "premium" (93 octane or higher).
Automotive gasoline is manufactured under a different ASTM standard from Aviation gasoline (there are several applicable standards, D4814 is commonly used), which permits different additives including ethanol (usually up to 10%).  

"Gasohol"

Gasohol is a slang term for automotive gasoline with any amount of ethanol blended into it, but these days it's often used to refer to blends like E85 (85% Ethanol, 15% gasoline stock).
Flex-fuel car engines and a few other specialty engines are designed to burn this fuel.



So what's the difference?

Why don't we burn highway diesel or heating kerosene in a 747?
In a word, purity. The additional controls imposed on Jet-A fuel by the associated standard produce a product with well-known properties. When you fuel a plane with Jet-A you can be confident that fuel won't freeze in the tanks at altitude (at least not unless you cold-soak it below -40 degrees). You also know the fuel will be "clean" and won't gunk up fuel filters or leave deposits inside the combustion core of the engine that can cause problems later.

On the other hand we don't burn Jet-A in a Mack Truck because it would be prohibitively expensive: Highway diesel doesn't have to meet the same strict tolerances as jet fuel, and theres no reason to burn a more tightly specified (and thus more expensive) fuel when a less expensive one is readily available.



The difference between Aviation Gasoline and Automotive Gasoline is a bit more subtle: the core blend stocks are extremely similar, but the additive packages are very different.

The biggest concern for aviation users is usually the ethanol commonly blended into automotive gasoline: Rubber components in aircraft fuel systems were not designed to handle alcohols, and can be damaged/degraded by ethanol.  

For cars the concern is the lead found in aviation gasoline. Any "modern" car (with a catalytic converter and oxygen sensors in the exhaust system) can't burn leaded fuel as the lead byproducts in the exhaust will foul both the catalyst matrix and the oxygen sensors (though a 1950s Plymouth Belvedere would have no trouble burning the stuff).

Work on an unleaded aviation fuel is ongoing - theoretically the fuel that comes out of that process could be equally suitable as a road fuel and an aviation fuel, however the chances of it making its way to your corner gas station are relatively slim, except possibly as a blend stock from batches that don't meet the final specification for a 100-octane unleaded aviation fuel, but are suitable for recycling into automotive gasoline blends.