Dark Energy is best described as an unknown energy that is in space. It causes the universe to get bigger at a faster rate. It is still in the stage of a hypothesis though according to the scientists. It was first discovered in the 1990s, so this term has not been around that long. Due to having gravity, there seems to be a discrepancy regarding the existence of dark energy. Therefore, dark energy doesn’t seem to have its own gravity.
Dark matter makes up most of the matter in the universe. It is believed that matter is anything that takes up space and has weight. Therefore, it seems to be true that dark matter does have its own gravity in the universe.
We are a long way from knowing the answer to this. Roughly 68% of the universe is dark energy. Dark matter makes up about 27%. One version of Einstein's gravity theory, the version that contains a cosmological constant, predicts that "empty space" can possess its own energy. Because this energy is a property of space itself, it would not be diluted as space expands.
As more space comes into existence, more of this energy-of-space would appear. As a result, this form of energy would cause the universe to expand faster and faster. We are struggling with areas of great mystery. To draw closer to knowing which if any of the dark energy possibilities are correct: a property of space, a new dynamic fluid, or a new theory of gravity - is to have more data, better data.