If Humans and Neanderthals are that far apart does it mean that higher intelligence evolved independently in multiple species? If Neanderthals had languages cap

If Humans and Neanderthals are that far apart does it mean that higher intelligence evolved independently in multiple species? If Neanderthals had languages capabilities (which I think is debated) then that may mean that human-like intelligence is not all that rare that we think it is. What implications does this have on intelligence evolving somewhere else in the galaxy (if any)?