These words tend to be used synonymously. But they are not at all the same.
Consider. what defines the Heavens? Blackness? Stars? Celestial objects?
What defines the Sky? Blueness? Absence of other objects?
The Heavens appear at Night. They are a place of shared community. The family of stars move around the sky together. Against these the wanderers go back and forth. This is not something that has been discovered since the invention of the telescope. They have always done this and we have long known about it. Long Long time. Not a thousand years or two but millennia we have watched these same events rise and fall, our very bodies carry the echo of life that has grown beneath these revolving endlessly same events. We measure Time and place by the Heavens. Even before the invention of the astrolabe and the sextant mariners were aware of where they were. They measured the stars so they could return home. But we, intoxicated with the latest invention, trying to prove ourselves to be modern and up to the minute, cannot believe that there are constants in our lives that have rolled on down the generations past the exodus from Egypt, past the building of the temple of Solomon, past the birth of Jesus and his demise, past the merciless persecution of one group of Christians by another, past the First world War and the Second World War and all the horrors they held and all of those that followed them, down to the invention of the calamitous mobile phone even past the murder of civilians by policemen. Still they revolve above us and will continue to do so even after the manic peppering of the sky with satellites, as if this conspiracy was unobserved. Even if the technologies we invent actually do scar the Earth, burn out the fine etheric mesh that hosts life and destroy the very life upon it, still those stars will turn about her.
The Sky is a different matter altogether. The Sky is a uniform colour and has only one occupant – the Sun. In dance we learn the importance of the vertical axis – individuation – and the horizontal axis – collaboration. The Sky is the place where I am the only important element in it. All others who appear there, and there are others, are subsidiary to me. None approximates to me nor rivals my presence. Those others include clouds and rainbows and of course birds. But all other celestial phenomena pale to insignificance against the beauty and splendour of the Sun.