What is the difference between Reformed and Presbyterian I feel like this is a dumb question, but maybe, just maybe, I'm not the only one confused by this.  Maybe if I'm willing to stick my neck out and look stupid, the answer will be here for those poor confused saps who come after me.

It seems like I often hear the terms reformed and presbyterian being used interchangeably.  When I'm speaking about the presbyterian church, or rather, the reformed church, or... I often stumble over my words because I feel like I'm probably saying the wrong thing.

I know that in a technical sense, reformed refers mostly to the theology and presbyterian refers mostly to the church government (or maybe I'm wrong about that too), but, in every-day parlance, what do you call a church who follows in the tradition of John Calvin?  Surely you can't go around calling them churches-that-follow-in-the-tradition-of-John-Calvin.  It's a bit of a mouthful.  If I call them Presbyterian churches, will someone think I'm foolish and think that I don't know what I'm talking about?  If I call them Reformed churches, will I be wrong?  Is it just a matter of only usually being right?  Does it depend on the denomination/association?

What do Christians who belong to such churches call themselves?  Do they call themselves Presbyterians?  Reformed Christians?  Calvinists?  All three?  None of the above?  Am I going to offend someone by using the wrong term?
There are Reformed Christians who are not Presbyterian (or at least wouldn't call themselves that), especially in the Dutch or Continental tradition such as the RCUS and URCNA. There are also Presbyterians that are not Reformed, such as many in the PCUSA, who would be better called "liberal". Further complicating the matter is that, as Brian Johnson pointed out, the word 'Reformation' would certainly include Luther, who would not now be called Reformed or Presbyterian. 

I would define someone who is Reformed as a "covenantal Calvinist". There are Calvinists who are not Reformed (such as Calvinistic Baptists like John Piper or John MacArthur or Mark Dever or Al Mohler, Jr.) I would define a Presbyterian as one who subscribes to the presbyterian form of church government, especially the plurality of elders elected by congregations and the connectedness of the wider Church. It is representative, like the American republic. 

You could argue, actually, that some of the Dutch Reformed denominations such as the RCUS and URCNA are presbyterian in their polity, and there's some truth to that, even if their names for things are a bit different. Still, the label isn't usually applied to them, because they subscribe to the Three Forms of Unity (the Canons of Dordt, the Heidelberg Catechism, and the Belgic Confession)  instead of the Westminster Standards (Westminster Larger and Shorter Catechisms, the Westminster Confession of Faith, the Directory for Public Worship, and the Form of Church Government). 

Indeed, the Westminster Standards typify what it means to be Presbyterian and Reformed. 

In summary: the words are not exactly synonymous, though they are certainly related in church history. 

The typical Reformed or Presbyterian, rather than getting all uptight about whether you're using the words accurately or not, would, I hope, just try to explain it to you! Labels can be helpful, but they are only labels; sometimes they are not so helpful.