HCCI, PCCI, RCCI, and GDCI are different combustion modes that have been developed to improve the efficiency and reduce the emissions of internal combustion engines.
HCCI (Homogeneous Charge Compression Ignition) is a mode of combustion where the air and fuel are mixed homogeneously and compressed until auto-ignition occurs. This mode is typically used in gasoline engines.
PCCI (Premixed Charge Compression Ignition) is a mode of combustion where the fuel is premixed with air and then compressed until auto-ignition occurs. This mode is typically used in diesel engines.
RCCI (Reactivity Controlled Compression Ignition) is a mode of combustion that combines features of both HCCI and PCCI. In RCCI, two different fuels are injected separately into the combustion chamber: one with high reactivity (such as gasoline) and one with low reactivity (such as diesel). The two fuels are mixed and then compressed until auto-ignition occurs. RCCI can be used in both gasoline and diesel engines.
GDCI (Gasoline Direct Injection Compression Ignition) is a mode of combustion that combines gasoline direct injection with compression ignition. In GDCI, gasoline is injected directly into the combustion chamber and then compressed until auto-ignition occurs. GDCI is typically used in gasoline engines.
A few points to add to the thorough description given by Ahmed above:
HCCI and PCCI are both suitable for CI engines. One main distinction of PCCI is that air and fuel are premixed, though not completely. In other words it uses a partially premixed (or stratified) charge, unlike HCCI, where the mixture is homogeneous. Stratified mixture is easier to achieve and may also help in controlling the onset of combustion to a certain extent.
There is also a combination of SI and CI modes, called SPCCI (Spark Controlled Compression Ignition). This is used in Mazda's Skyactiv-X engine.
Here a small quantity of air-fuel mixture is ignited by spark, but the resulting high pressure and temperature causes autoignition of the rest of the mixture, which is usually ultra-lean.
In RCCI, the LRF (e.g. gasoline or another low cetane fuel) may be injected in the intake manifold or port, while the HRC (usually diesel / biodiesel) is injected into the combustion chamber. Varying the LRF:HRF ratio is useful for controlling the start of combustion.
In HCCI, the charge is completely premixed. To create concentration stratification, PCCI was suggested. A significant part is early injected preceding the compression stroke to make a premixed charge, then a portion of the fuel is introduced close to TDC. More details in these articles
Article Investigative research of diesel/ethanol advanced combustion...
Article A comparative study for the effect of different premixed cha...
Article Fuel Reactivity Controlled Compression Ignition Engine and P...