Arthur Miller wrote plays with well-developed themes focusing often on the conflict between an individual's responsibility and his or her deepest weaknesses.
Both The Crucible and Death of a Salesman deal with this conflict. One play looks at the social effects of individual (moral) decisions and the other looks at the effects of one person's weaknesses on a family unit.
Each play, at its heart, is concerned with illusion and delusion as methods of coping, as intentional deception and, importantly, as symptoms of personal emotional weakness.
What appears to be true to the characters in Death of a Salesman is often a far cry from reality, and this is communicated numerous times throughout the play.
We can see this dynamic in The Crucible as well.
For The Crucible, deception and illusion are obvious in their importance to the story of the play. Abigail and her friends spread lies that lead to witch trials and death. Those who choose to stand up to the lies are examples of characters taking personal responsibility for the actions of the community, attempting also to suggest that the young women and judges should realize what kind of moral decisions they are making.
Proctor and Hale are two characters in the play preaching personal responsibility which means also that they attempt to dispell the illusion under which the town has been working.
In Death of a Salesman, Willie Loman is also subject to illusion and deception, but his deception is self-induced. He is unwilling to take responsibility for his failure as a father and as a salesman and so clings to the dream that he was once a great salesman, widely liked and widely admired. The fog of his dream is purposeful and functions as a defense against accepting his responsibility. Only Biff tries to force Willie to face the reality of his life and his failure, and in this Biff fails.
The themes of these two plays can be connected in the above ways but the form of each play is very different. The prose sections and historical information of The Crucible make this play longer and, arguably, more allegorical than the psychologically driven Death of a Salesman. Also, Death of a Salesman features a small set of characters compared to The Crucible, focusing largely on Willie Loman and his relationships. The Crucible, while focused largely on Proctor and his relationships, presents a wider interest in the play's secondary characters like Elizabeth, Abigail, Parris and Hale.
Beyond the obvious differences in time period, these plays also differ in subject. We might refer to the subject of each play as a thematic subject with Death of a Salesman tackling the problems of the American Dream and The Crucible examining moral corruption among the "professed righteous".