Soft synth vs hardware synth: They both do similar things, but in the soft synth, you buy a program that runs on a (modified) general purpose computer instead of the program being built into a keyboard or module.
They are more like a hardware module than a keyboard - MIDI in to play them, but no keyboard.
The computer - some for PC, some for Mac. Notebook computers used frequently for more portability. Many of the soft synths need a powerful computer with high processor speed and considerable RAM.
Modifications: Very few notebooks come from the factory with full MIDI capability. Some keyboard controllers have USB connections, which will work with most standard notebooks. However, the built-in audio in most notebooks has too much latency to work well with a soft synth in live play. Latency is the amount of time betwen when MIDI sends a "key depressed" signal, and sound comes out. It is usually meausred in milliseconds (one thousandth of a second). Latency over 30 or so milliseconds becomes quite noticable, and most standard notebook audio systems have latency like several hundred milliseconds (example 500 milliseconds - push a key down, it sounds half a second later - that is a LONG time in a fast song).
I used Native Instruments B4 software for Hammond/Leslie simulation for about a year and a half. Had a powered docking station at the church with the special ASIO midi/sound card, carried the notebook computer to church; used an eMu XBoard 49 for control. Sounded good, but logistically - I had to boot up the computer, load the software, select the presets - all this took time. Changing sounds on the fly when playing live - I could program the knobs on the eMu (usually had them set to simulate "drawbars"), but no where near as convenient as selecting another preset on a hardware keyboard.
I have retired the system, and currently use a Kurzweil PC2 keyboard with the KB3 module to simulate the Hammond/Leslie sound. I just turn it on - 20 seconds later it is ready to go, it is easier to control in live performance (and I have lots of other sounds available instead of being limited to just B3 type sounds).
I also had PRO52, which emulates a Prophet 5 vintage synth, and eMu Proteus X, which emulates the vintage Proteus synth. Couldn't run them all at one time in a live environment.
My own conclusion: soft synths work very well in a recording studio environment; they have considerable drawbacks in live performance situations.
Jim