Basically in Multi-Agent System we try to characterize more the agent's properties and to define the negotiations between agents usually to solve a problem, but it doesn't have to be an optimization problem, for example planning, costs/profits, a good example of MAS is used for electricity markets.

On the other hand, Agent-Based Models, which could be PSO, Ants and the like, are more intended to solve an optimization problem. Furthermore, ABMs also try to find/simulate emergent patterns that arise from the interaction between the agents and their environment. In other words, ABMs are also used to explain the complexity from the micro to macro level.

Does it mean that in swarm based algorithms a single ant/bee/particle cannot communicate and/or negotiate with other ants/bees/particles?

Yes, they do communicate, but basically by interacting with their environment. For example in ants, communication among ants is achieved by leaving some information (trails) there where they were already looking for a solution for the problem (pheromones). So other ants can use this information to either continue looking on that direction in case the signal is a positive one or to avoid looking for a solution on that direction in case the signal is a negative one.

Multi-agent systems works more like a committee machines (more jargon right!...) let me explain - Rather than having one machine or system make the decision, the decision will be made by consensus(average) or weighting(fuzzy) and so on of all the machines in the "committee".

Particle Swarm Optimization - It's more of an evolutionary algorithm. Optimization follows the idea or concept behind biological swarms like bees etc. and the system can come to internal description or solution on its own.