It seems that a LPF is contained in PLL and not in frequency-synthesizer. Maybe I had made a wrong judgement.
A PLL is a specific type of building block, that will control a variable oscillator (usually a VCO, though it doesn't have to be voltage-controlled - YIG-based PLLs use current instead) such that it's phase is locked to that of a reference (not frequency! It just so happens that if you lock to a phase, you automatically lock to the frequency too).
Of course, they can put multipliers and dividers in between to have the oscillator frequency and reference frequency be different, but they are always 'locked' to one another.
A frequency synthesizer is the name we give to a block that synthesizes frequencies. This can be done internally through a PLL, but this could also be an FLL (frequency-locked loop), DDS (direct digital synthesis, basically a DAC that just outputs a signal at the frequency we want), DLLs (delay-locked loops), etc...
In modern electronics the entire thing is not always as simple as it may seem, and many high-performance synthesizers may use hybrids of different types.
So this question is kinda like asking 'What is the difference between a Car and a Vehicle?' - One is a subset of the other, so you can't really speak of 'differences'.
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.
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.
"Frequency synthesizer" is just a more general term than "PLL". Every PLL is a frequency synthesizer but not vice versa.
A PLL is one common type of several possible types of frequency synthesizers. Often frequency synthesizers are PLLs but not every frequency synthesizer is a PLL.
An example for a frequency synthesizer that is not a PLL would be a Direct Digital Synthesizer (DDS).
examine the block diagram of a PLL
and we find the LoopFilter output may be useful for extracting Frequency Modulation.
On the other hand I've seen Frequency Synthesizers, in the 130--180MHz range, have voltage inputs for sonar information from submarine-tracking piezo sensors. The sonar voltage was inserted into the LoopFilter voltage of the embedded PLL.