Hi Bart!
Nice to know you want to sound like Symphony X
Well, to answers your questions, when it comes to electronic music instruments, you get many 'things' which performs certain functions and these 'things' don't always have to be the same piece of hardware. The midi protocol is used for these things to communicate with each other in almost anyway that you can think of.
A synth is a module which generally has alot of effects and features for creating and modifying sounds. Generally dedicated synths you find as seperate modules or as part of keyboard don't have latency problems. A software synth on a computer could pose a problem if you have a slow piece or bad software.
A sampler is a module that allows you to record a sound at a certain pitch, and then have that one sound modified to other pitches so you can get the full range of a 'real' sound across the whole keyboard.
Sound modules or libraries are generally huge databases of already existing sounds such as piano, drums, strings, guitars and so forth. These are usually either generated through a synth(uses less memory, found on the cheaper end) or are pre-recorded sounds(more memory, generally more expensive). Generally better for creating already existing sounds like strings, orchestral instruments that having to try very hard to create those sounds yourself with a synth.
A sequencer is a module used to record the music electronically, as in play this note this hard at this time with this effect etc... unlike analog recording which records the pure sound waves.
A midi controller is any device which is used to play the music, and is useless on it's own and needs to be plugged into a synth or sound module. This is usually in the form of a keyboard(as in the black and white keys), but can be in any forms imaginable, assuming there are companies that produce them. I have seen drum pads, keytars, pedals and accordians so far as midi controllers
.
Most 'keyboards' come with a combination of these features to varying degrees of quality, although there are some trends which gives rise to their common names.
A workstation is generally a keyboard with all these features built in(all in one piece of hardware) at good quality you can use to record semi or fully professional. If you want more info on these ask Sysryn, he knows alot more about these babies than me(they are all outside of my price range for now, so I havn't looked at them much yet).
Computers can generally perform any of the functions mentoined above, but as a controller and synth you will have the most trouble due to lack of versatility in the controller sense and cpu restrictions on the synth side.
Generally, there is alot of versatility in the way you can use the various parts and 'things' together. For example you can hook up a controller to sound module which goes through any number of synths to modify the sound which then passes it's info to speakers and sequencer.
But when buying anything, here is some advice I generally adhere to:
First find out what is possible(hopefully this post so far gives you a good crashcourse). Then find out what is available, for this you will just have to do alot of research and read up alot of specs on products. Then find out what you want to do, will it be recording/live performance, who will do it. Then you set the budget you will use and start narrowing down the models and modules you will consider. Then you study the narrowed down selection in great detail, read reviews(both formal and user). Then you look for demonstrations of what it can do, generally you can narrow it down more by doing a search on the model number on youtube. Lastly, you go to your local music stores and try out the products extensively to make sure you will want to spend money on buying it.
But, regarding the best I can deduce about your situation from your post:
Regarding the GR-20: Personally, although it has great potential, that potential isn't reliable. Reviews for it is mixed with people that love it and other that say they get poor results. If you try this take your exact setup you are going to use to play with/record with and test it out in a store before you buy. Since from what I can tell it analyzes the analog signal from your electric and converts it into digital information for use with the synth, the quality of the signal conversion has too many variables, this is only something I would buy for fun, but not for $500. If you are going to use it as a standalone synth with a seperate midi controller, you might considering just buying a dedicated synth or sound modules with a midi controller.
If you want to use keyboard related instruments for metal music, especially Symphony X style with choirs, strings and so on, and assuming your budget to be around $500, in my opinion it would be better to buy a sound module/library and midi controller in that price range. You can get a very good keyboard midi controller for around $180 and spend the rest on a good sound module or synth.
Or if you don't already have one, recruit a keyboardist! If you want that kind of sound in your band it would be a wise thing to do, especially if you plan to play live(which is what metal bands do).
Just a last disclaimer, I'm rather new to the technical side of keyboards, but that is what I have been able to deduce so far about the general way in which instruments of this nature work.