Imaduck, you're a bit off there, and bennychico11, your answers are sometimes a bit askew (the one about MIDI messages sending a "1" to start a note and a "0" to stop it, for example) and this one is no exception.
A synthesizer is not a sound. A synthesizer is a musical instrument that uses some form of synthesis to create sounds. Most commonly it take the form of a keyboard as a way to play its notes, but that's not necessary.
Synthesis in its most general usage means "the composition or combination of parts or elements so as to form a whole." In this context, synthesis means a method of combining and manipulating electrical signals to make a musical sound when sent out through a speaker.
The common methods of synthesizing sounds are additive and subtractive synthesis, wave table synthesis, FM synthesis, and physical modeling synthesis. The sounds that are made are themselves are called, well, sounds.
Samplers are musical instruments that use actual recorded sounds as their building blocks. The line between synths, especially wavetable or sample-playback synths, and full-on samplers, is a bit blurry. Usually the distinction is a sampler allows you to actually record the sounds you use for building blocks themselves. The actual audio data is stored in some way, in persistent memory or otherwise, and these stored sounds are often referred to as sound banks.
In the case of FM synths and others that don't use actual recorded sound as building blocks, the sounds don't exist as stored audio per se, they are created by the synthesizer's electronics via whatever algorithm they are using while you play it. The instructions are saved as a program or preset.
All synths have presets in the sense of default sounds they make without your having to do any manipulation or programming. The depth of editing options varies from almost none (play the preste sounds only) to almost total control of nearly every detail of the sound, including blending and stacking multiple sounds. But they're all synthesizers.
Because of MIDI, a protocol for communication between electronic musical intruments that pretty much all producst support, the various components can be distributed -- hence the synths in a box with MIDI ports but no direct way of triggering sounds, and keyboards that are controllers only, sending out MIDI messages but having no actual sounds themselves.