Judaism, like all religions thousands of years old, includes many people holding many different beliefs over time. Many people think that religions are monolithic, and that they have one set of beliefs. Actually all religions are composed of different believers with diverse ideas and beliefs.
I would say that the best sense of what the Jewish belief in Satan, the Adversary is, is to be found in the book of Job. Satan is "the adversary" but he is not disobedient to God. He must ask God's permission before tempting a righteous human being, or making him suffer. Nowhere are the beliefs about The Adversary laid out clearly, but this gives us a hint. It is not clear whether the Adversary tempts or punishes those who are not righteous, but it seems so, as the afflictions given Job are seen as punishments usually applied to the unrighteous. And it is not clear if the Adversary can do this to the unrighteous without asking God's permission.
So, what we can know from this is that the Adversary in Judaism is very different from the Christian Satan. He is not the Adversary of God, but an obedient, if controversial, angel. He brings adversity, normally only to those who are not righteous. Thus he is a personification of an aspect of God's justice.
In general, in Judaism, it is God who inflicts, or allows angels to inflict, punishment. There is no angelic being at war with God, and thus, there is nothing like the Devil as he is usually seen in Christianity, a rebellious angel who rules life on Earth or in Hell.
Also, the Angel of Death is not the same as the Adversary, and the being who brought death to the firstborn of the Egyptians to help free the Israelites from Egypt was not the Adversary. So the Christian association that all these figures are one or closely united is not part of Judaism either.
It is also fair to say that many Modern Jews, like many Modern Christians, do not believe in the Adversary or the Devil at all.