What is the difference between a PLL and a frequency-synthesizer？
According to Wikipedia a frequency synthesizer


  is an electronic circuit that generates a range of frequencies from a single reference frequency.


A block schematic could look like:



And I see a Lowpass Filter in there so your statement


  LPF is contained in PLL and not in frequency-synthesizer.


is untrue.

Also a Phase Locked Loop (PLL) has a block schematic which is a copy of part of the frequency synthesizer:



So basically a frequency synthesizer could be a PLL but with some blocks (mainly frequency dividers / counters) added to increase the range of supported frequencies.

A frequency synthesizer can also be made using a DDS which has no PLL.