difference between frequency syntesizer & frequency generator

Is the same difference as between PLL and Oscillator.

Both are frequency generators but a synthesizer is a complex system in which a computer generates a string of preset frequency values. An "ordinary" signal generator usually has a tunable oscillator over a specified band; you can tune the frequency to any within the band. Some synthesizers cannot tune smoothly over a band, they only "sit" on the preset frequencies.

Synthesizers use a reference frequency generator from which the computer generates the output frequencies. Frequency stability, phase noise depend then on the reference generator; the system can be more stable and have a lower phase noise than ordinary tunable generators.

"frequency generator" is a pretty generic term--it could mean many things.

"frequency synthesizer" pretty much always means some sort of frequency generator that is locked to a low frequency reference clock. When you lock it, its "jitter" gets reduced, and its frequency accuracy gets greatly improved. For instance, a synthesizer that is tuned to 10 ghz probably is at 10 GHz +/- 1 KHz

If your "frequency generator" is a sweeper, it probably has a much bigger frequency inaccuracy, and probably has worse "jitter". It might have better spurious signal outputs though, as it is probably the direct output of a YIG tuned oscillator. A sweeper tuned to 10 ghz probably is at 10 GHz +/- 20 MHz.