Homogeneous Operation
Fuel is injected during the intake stroke.
This mode of operation is similar to port-injection in that air and fuel are mixed homogeneously to achieve a stoichiometric ratio, albeit with some important differences:
There is no mixing of air and fuel across the intake valve.
In vanilla GDI setups, the fuel is injected directly into the combustion chamber. Consequently, the intake valve does not play a role in the mixing of air and fuel.
(In fact, some manufacturers have found GDI engines suffering carbon build-up problems on the intake valves due to the lack of fuel hitting the backs of the valves)
There is much less time for the mixing to take place.
With port-injection, fuel can be injected throughout 720° crankshaft rotation.
GDI demands a much narrower injection window (180° crankshaft rotation - induction stroke only).
Fuel pressure is much, much higher
The narrower injection window demands this in order to deliver the required amount of fuel in less time. This brings an additional benefit of increased combustion chamber turbulence, which helps to promote more complete air-fuel mixing.
Stratified-Charge Operation
Fuel is injected during the compression stroke.
In many ways, this operating mode goes against the grain of common thinking.
Rather than focus on getting a thoroughly-mixed, uniform air-fuel mixture, the idea here is to get just a fraction of the intake air to interact with the fuel around the spark plug.
By stratifying the charge, the ignition timing can also be delayed.
There are a couple of benefits:
Less risk of engine knock
The excess air surrounding the air-fuel charge ("stratified" charge) helps to cool down the combustion chamber, reducing the likelihood of knocking, enabling higher compression ratio.
Fuel-savings
This mode allows the engine to sip fuel. It allows for delayed spark ignition without the risk of engine knock, which results in higher torque for a given amount of fuel.
This mode of operation is ideal for part-throttle conditions, such as when cruising at steady-speeds.