Blackberry or raspberry?

Well, there's a simple answer and a more complicated answer. Both are species (more than one) in the genus Rubus, but it has hundreds of species that also includes dewberries, cloudberries, salmon berries, thimble berries, and more, including many hybrids like boysenberry. Locally it's a bit easier. Raspberries, both cultivated and wild, red, black, orange, purple, or gold, are thimble shaped; the drupelets pull free of the receptacle, so the fruit is hollow. The receptacle stays with the drupelets on blackberries, which often are more elongate in shape. The brambles are similar, as are the flowers, but our raspberries have a powdery-waxy coating on their stems which easily rubs off. Blackberries lack this. TPP is uncertain whether this holds true for all species bearing those names or not.  But here in eastern N. America, that works. Blackberries are of course dark purple-black, but so are our wild black raspberries. So there you go. That's the simple version.

A berry pragmatic change in color

For several years TPP has tried to grow blueberries here in the alkaline clay soil, heat, and droughts of the midwest. Let's make a long story short; blueberries don't like these things.  Having condemed quite a number of blueberry plants to death, not without giving them a chance to make it, last summer's heat and drought was sort of the last straw.  Nothing remained but the not-acid-enough soil.  In a bit of impulse shopping, TPP decided that the thing to do is to change color, from blue to black.  Both blue and black make a pretty decent pie.  Both can make a jam or jelly.  But the Rubus will be much easier to grow especially because the modern varieties are thornless.  In the old days picking blackberries was an invitation to considerable injury and probably an infestation of chiggers.  In particular these were very vigorours looking plants, so blue was changed to black.  Now we shall wait and see.