I think a good analogy is with creating images.
There are lots of ways to create an image: with a pencil, with a fibre-tip pen, with oil paints, with chalk, with oil paint, with watercolours, with photography, and so on.
Of course, you can photograph an oil painting, but that doesn't help you modify it in an oil painterly manner.
You can't accurately reproduce a chalk drawing with oil paints, and you can't accurately reproduce an oil painting with chalk.
Similarly there are lots of ways to create a sound: with an acoustic instrument, with an electric instrument, with additive analogue synthesis, subtractive analogue synthesis, FM synthesis, sampling, and hybrids of all of these.
Of course, you can sample any sound - but that doesn't help you modify it in a way that's consistent with its origin. You can record a guitar note, but you can't make something that sounds much like a guitarist playing, just by playing that one guitar note at different pitches.
Different synthesisers use different methods to create sounds, and so in general you can't just transfer a sound from one synthesiser to another.
However, think of a tool like Corel Painter, which gives the digital artist a palette of simulated pencils, simulated oil paints, simulated chalk, and so on. This comes close to letting the artist recreate images created in all those mediums.
If you use a computer as your synthesiser, you have the ability to use thousands of software simulations of different kinds of hardware synthesiser. These are typically made available as plugins, which can be controlled by music software like GarageBand, Logic, Ableton Live, Cubase etc.
So for example, if you want a sound like that of the classic Roland TB-303 synth, you can choose from a number of plugins that simulate the circuitry of a 303; or you can pick a plugin you already own that simulates a synth with similar properties to the 303, and try and coax that into making a 303-ish sound.
So, you can make your PC or Mac simulate almost any kind of synthesiser. But different kinds of sound are likely to need you to acquire different plugins.