The term only exists in notation software and was devised as a clever shortening of the full term by some dude in marketing who thought that by making it sound like something unique, they might attract more buyers. So I don't recommend using it. Calling a software synthesizer a "soft" synth in a crowd of synthesists will get you ridiculed. Also, there's no such thing as a "hard" synthesizer — it's just a hardware synth or software synth. One is a physical machine, the other is a computer program.
Connor is, respectfully, wrong about VSTs. In the world of software instruments, the way that you use a particular thing is (most often) by integrating it into your audio software as a plugin. These plugins come in a variety of different formats, only one of which is VST (think of the formats as file formats — like MP3 or WAV). Not all VSTs are software synthesizers though. A virtual instrument plugin can produce sounds a number of different ways, the two most common being synthesizers and samplers.
A synthesizer is — very very basically — a piece of software that emulates the original hardware technology that creates sound based on advanced manipulations of very basic waveforms (sine, triangle, pulse, etc.) A sampler, conversely, does not generate its own sound. Instead, it acts as a very advanced 'player' of pre-recorded audio material. Garritan and the Vienna Symphonic Library are both sample libraries, and as such they integrate into your audio software as sampler plugins. They produce sound by calling up pre-recorded material rather than generating the audio themselves.
If you're using notation software exclusively to write your music, then none of this kind of stuff really applies to you. It only becomes meaningful when you start working in a proper DAW (Digital Audio Workstation) with the intent of creating realistic mixes on your computer.