In Calvinist circles, the term "common grace" is used to describe a number of things. One definition provides three aspects:
1) "a certain favor or grace of God which He shows to His creatures in general;"
2) "the restraint of sin in the life of the individual man and in the community;" and
3) an influence in which, "God, without renewing the heart, so influences man that he is able to perform civil good" and, thus, "the unregenerate, though incapable of doing any saving good, can do civil good." (source)
In contrast, Wesley (one of the most influential Arminian writers) defined prevenient grace thus (I'm not sure whether these are Wesley's own words or a distillation of his thought ... they seem to be accurate, and I could not find a more pithy quotation directly from him.):
Human beings are totally incapable of responding to God without God first empowering them to have faith. This empowerment is known as "Prevenient Grace." Prevenient Grace doesn't save us but, rather, comes before anything that we do, drawing us to God, making us want to come to God, and enabling us to have faith in God. Prevenient Grace is Universal, in as much as all humans receive it, regardless of their having heard of Jesus. It is manifested in the deep-seated desire of most humans to know God.(source)
One could loosely compare the two by saying that common grace simply places a limit on the depth of man's depravity, whereas prevenient grace removes man's depravity. Common grace makes man not as wicked as he otherwise would be, but prevenient grace makes man essentially morally neutral.
The two are quite different. It's worth noting that some Calvinists use the term "common grace" to refer more broadly to things like the fact that God sometimes gives common physical goods to both regenerate and unregenerate alike (for example, God may give rain to water the crops of both a god-fearing farmer and his neighbor the god-hating farmer). Other times, people use the term "common grace" to refer to the outward restraints on human wickedness, such as civil government and parents.
Likewise, prevenient grace is sometimes given a range of meanings. I've heard the preaching of the gospel referred to, by an Arminian, as prevenient grace. Indeed, some Arminians would say that every favor or opportunity that God gives to man before he believes, prevenes (goes before) that faith, and consequently can be labeled prevenient grace.
Thus, while the central meanings of the two terms are largely unrelated, there is occasionally overlap, where a Calvinist might loosely refer to something as "common grace" and an Arminian might loosely refer to it as "prevenient grace."
I should point out that not all Calvinists agree with using the term "common grace." I understand the historical, linguistic, and logical rational for that disagreement (I think), but I view it as a scruple. I'm not going to debate the issue here, and I hope that I won't unnecessarily offend my scrupulously Calvinistic friends by referring to their views that way. On the other hand, I don't endorse the idea of saying that a person is a "hyper-Calvinist" if they don't use the term "common grace," or find the three points above to be an inaccurate statement of doctrine. I realize that puts me at odds with such notable contemporary bloggers as Phil Johnson, but that's just something I'll have to live with. And I'm not going to debate that issue here, either.
Having explained the differences between "common grace" and "prevenient grace," I hope I will have answered my reader's question.