EDIT: Question simplified:
- What is the difference between frequency generator and frequency synthesizer. 
- What is the difference between clock generator and clock synthesizer. 
EDIT: Question simplified:
What is the difference between frequency generator and frequency synthesizer.
What is the difference between clock generator and clock synthesizer.
 
    
     
    
    Synthesizer usually is a more complex device than generator. Synthesizer consists multipliers, dividers and mixers to generate desired signal. Generator is typically a device that generates signal with fixed parameters.
Check out the ICs. For example: http://www.digikey.com/product-search/en/integrated-circuits-ics/clock-timing-clock-generators-plls-frequency-synthesizers/
