You can find your answer in videos like this:
In short, FreeSync is AMD, G-Sync is Nvidia. If you have a G-Sync monitor, you need an compatible Nvidia GPU to enable G-Sync. Up until recently, similar rule was applying to AMD GPUs and FreeSync monitors. But unline G-Sync, FreeSync monitors are cheap. To compete againts this, Nvidia announced that they will give support for some FreeSync monitors. That's where G-Sync Compatible coming from.
Except from G-Sync monitors are more expensive than FreeSync monitor counterparts (they have a specific part to compute adaptive syncronization meanwhile FreeSync monitors don't, "Free"sync), these two technologies are identical.