There was once such a thing [as Standard Generic Democrat], but not for quite some time.

There still is. But the Standard Generic Democrat changes over time, because the party (and the country) changes over time. Today's baseline "standard" Democrat is going to have vastly different positions on things like gay marriage and immigration than the SGD from thirty years ago, for example. And of course, every actual Democrat will differ in some degree from the Standard Generic Democrat.

But they'll all come close. For the most part, the positions of most Democrats will hew pretty closely to the standard party positions overall. The (D) next to a candidate's name is a really good heuristic on what their positions are. For example, both Obama and Biden were pro-union. Their positions on most things were pretty much the same. At the edges, there might be some differences - but their core stance on unions (they're good! they should be encouraged and protected!) will be the same.

Where they differ, though, is not in their positions, but (dare I say it?) in their priorities. Obama supported EFCA. He and Biden had the same position on that issue. But health insurance reform and banking reform were higher priorities for Obama than EFCA - so they went first, and received most of his political capital. Biden might have structured his priority list differently, had he been President with a supermajority in 2008. He might have insisted on EFCA before the health care law - not because he had a different position on the bill, but because it was more important to him. Obama was the health care guy, and Biden's the union guy - which doesn't mean that Biden didn't support health care reform or that Obama doesn't support unions. Just that they prioritize the issues differently.