Swarm Intelligence refers to the characteristic of the system under consideration, which may be either natural or artificial. Key elements are self-optimisation, decentralise and that collective behaviour. You find swarm intelligence in swarms of birds or fish, without considering computer technology at all.
If you apply algorithms, such that computational systems like multi-agent systems exhibit this kind of behaviour, than you talk about swarm computing. You can then mimic natural systems to study them, or you can apply swarm concepts to problems like optimisation.
Swarm computing doesn’t entitle presence of intelligence. Otherwise, intelligence can be considered as a special case of computing.
The main idea of swarm intelligence is that each unit in a swarm is simple and follows a small rule set dealing only with its own adjacent environment. Swarm intelligence is the collective behavior of decentralized and self-organized systems. It consists typically of a population of individuals interacting in network with one another and with their environment. The inspiration often comes from nature identical biological systems.
The implementation of Swarm algorithms is termed as Swarm Computing.
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