Satan (שָׂטָן) in Hebrew means “enemy” or “adversary” but this “opposition” is in the Old Testament directed in the specific sense of an “accuser”. The idea seems to be that since man has fallen into sin under the curse of Law, the Devil appeals to God’s own justice in order to accuse men and keep them under his domain of death. He is a kind of 'receiver of souls' that are 'obnoxious under law' and 'resigned to death'. For example, when God was about to restore the exiled church back into Jerusalem, Joshua (meaning savior) the high priest was a symbol of the ministry of the church promised to be restored from exile. However, Satan opposes this restoration of this ministry through 'accusation'. Possibly because of the sins of the Joshua, the priests and the people, Satan accuses Joshua as their representative, demanding they remain dead under the broken Law. The Lord intervenes and rebukes Satan in his accusations against God’s people.
Then he showed me Joshua the high priest standing before the angel of the LORD, and Satan standing at his right side to accuse him. The LORD said to Satan, "The LORD rebuke you, Satan! The LORD, who has chosen Jerusalem, rebuke you! Is not this man a burning stick snatched from the fire?" (NIV Zechariah 3:2)
This is the same way in the case of Job, which was mentioned in the question. In Job 2:3-5 Satan 'accuses Job' saying that he was not a good man as God had said, but that if God would remove his protection he would be as wicked as the rest and ‘curse God’s face’.
In the New Testament Satan (Σατανᾶ) carries the same meaning. In the New Testament we see this opposition is even more clearly defined by his role of 'accuser'. For example, the Devil wants to ‘sift’ Peter just like he did Job:
"Simon, Simon, Satan has asked to sift you as wheat. But I have prayed for you, Simon, that your faith may not fail. And when you have turned back, strengthen your brothers." (NIV Luke 22:31-32)
This is very similar to Job’s situation but the Lord rebuking Satan is replaced by our Lord’s intercessory prayer, clarifying the roles in a clearer light than found in the Old Testament but without deviating from the original concept.
In the case where the Devil opposes Christ directly he can’t be properly accused, as he is sinless, yet the opposition is like an accusation. According to the flesh Christ’s willingness to die was not right and so Peter’s in his rebuke of Jesus is still an accusation, only according to the flesh. However, is not that the same case with all the Devil’s accusations? Though we be guilty, yet when accused by Him, it is a lie!, for in Christ we are righteous. This is why Revelations has the bottom of the matter spelled out:
Then I heard a loud voice in heaven say: "Now have come the salvation and the power and the kingdom of our God, and the authority of his Christ. For the accuser of our brothers, who accuses them before our God day and night, has been hurled down. They overcame him by the blood of the Lamb and by the word of their testimony; they did not love their lives so much as to shrink from death. (NIV Revelation 12:11)
Therefore, Satan is a stumbling block and opponent in his accusations and these two aspects of his person are complimentary, not divergent.