A diesel engine, operating at a much higher compression ratio, uses the heat produced by compression to ignite its fuel. A diesel engine, therefore, does not have spark plugs, nor the related ignition system found in a gasoline engine.
Other than this, diesel engines are very similar to gasoline engines, operating on the same principles, and existing in more or less the same variations.
In a gasoline engine, a mixture of gasoline and air, controlled by a throttle, is inducted into a cylinder. Some engines use aftermarket cold air intakes to gain horsepower, torque, and throttle response. This is compressed by a piston and at optimal point in the compression stroke, a spark plug creates an electrical spark that ignites the fuel
Gasoline engine
Diesels do not need an ignition system - no coil, distributor, or spark plugs - but instead depend on the heat of compression to burn fuel. Before the engine is hot, "glow plugs" can be used to start combustion, but they are not timed like spark, they just stay hot. 
Gas engines control power production with a throttle that reduces air pressure in the intake manifold so less air and fuel get into the cylinder. Diesels have no throttle (this gives them a small efficiency advantage), they control power by pumping less fuel into the cylinder.
Gas engines add fuel to the air before it enters the cylinder, diesels spray it directly into the combustion chamber after compression - except small two-strokes.
Because of the differences in how they operate, diesels are typically designed for lower RPM peration and higher low-end torque and are almost universally turbocharged in production cars and trucks. Gas engines (especially with smaller displacements) are typically designed for higher RPMs and get higher torque and horsepower by filling the cylinders more times each second. There are exceptions, but this is most common in mass-produced engines.
For convenience I have summurised the above description:
Gasoline Engine-(GE)
Diesel Engine-(DE)
1. Spark plug is used to ignite the fuel.--------------------------(GE)
1. Spark plug is not used, i.e. no ignition system is used. --------(DE)
2. No fuel injector is used.--------------------------------------(GE)
2. Fuel injector is used to spay fuel into the cylinder in compression stroke.--------------(DE)
3. Power production is controlled with a throttle valve that reduces air pressure in the intake manifold, so less air and fuel get into the cylinder.--------------(GE)
3. No throttle valve is used, power is controlled by pumping less fuel by injector.---------(DE)
4. Fuel is mixed with air before entering the cylinder.----------(GE)
4. Fuel is sprayed directly into the combustion chamber after compression stroke.--------(DE)
5. Typically designed for higher RPM and get higher torque and horsepower.-------------(GE)
5. Typically designed for lower RPM operation and higher low-end torque.---------------(DE)
