SI is SPARK IGNITION - Otto (4-stroke) and Day (2-stroke) cycle
CI is COMPRESSION IGNITION (DIESEL) also in 4- and 2-stroke variants
The SI spark plug is timed to start combustion at the ideal moment, usually some degrees before the piston reaches the top (TDC or Top Dead Centre). The burning mixture then drives the piston down for the power stroke.
The CI fuel is injected (sprayed) into the cylinder at the ideal moment - this too is usually some degrees before TDC, and the red-hot air in there then starts the fuel burning. This then drives the piston down for the power stroke.
SI is limited in maximum compression ratio (the amount the air or mixture is compressed as the piston rises in the cylinder), or it can start to behave like CI (Dieselling).
CI uses the highest compression ratio possible to improve ignition - and - improve efficiency too... The expansion ratio is the inverse of the compression ratio, and the more that the burning gas is allowed to expand whilst doing work, the better the efficiency.
CI is also an 'excess air' cycle, potentially. A full cylinder of air is compressed each time, and the amount of fuel injected is varied to change power - this is beyond the lean burn that can be achieved with SI.