A synthesizer is purely a sound generator. That's 'all' it does. It provides you with different types of basic waveforms which you can then mix together and manipulate in many different ways to create a massive palette of different sounds.
This is how sound is created in the 'real world'- a bunch of different sound waves generated by a source and mixing together in the air.
Synthesizers attempt to recreate or 'synthesize' that process.
There are a few different forms of synthesis, the basic ones being additive, subtractive and FM.
An 'arranger' and by this I guess you mean sequencer, is a tool that allows you to construct a pattern of sounds over time in a linear fashion.
There are stand-alone hardware sequencers that do this job and this job alone, or there are software sequencers that today have evolved to perform many other functions as well, a la Cubase, Logic, Sonar etc etc.
A workstation is a unit that pulls both of these functions, as well as many others (sampling and cd burning for example) into one hardware box, often with a keyboard in place too, so you can effectively produce a track using nothing else.
They can be very refreshing to work with because you can get to know the unit and its functions very well and very quickly, but can also be limiting because you are stuck with whatever feature set the designers chose for that particular model of workstation, and memory can only be expanded so much, so you can't have the kind of monster setup you could by combining individual elements in one organic system.
I can see the attraction with workstations but was never tempted to go that route.
Choosing a software sequencer, which will nowadays include a sampler far more powerful than any hardware alternative, and a good hardware synth as well as software synthesizers based on a powerfulcomputer core is generally considered to be the best approach, but there are still many people that like to work just in the one box.