Clearly, this is a case of "Taxonomists Gone Wild" or, more specifically, one taxonomist gone wild ... Mr. Liberty Hyde Bailey.
L.H. Bailey was an incredible man who lived at the turn of the century 1858-1954. I won't go into much detail about him, since I would only get it off the internet, so you can take a look here and here.
The bottom line is that he studied the Rubus genus in detail, as well as some others, and as one person put it, "L.H. Bailey never met a Rubus he didn't like to call a separate species". The Rubus genus has been split and lumped a hundred different ways. Even Charles Deam couldn't sort out the Rubus genus, he sent all of his specimens to L.H for analysis!
So, how to tell them apart? The main categories are Blackberries, Dewberries, and Raspberries.
Raspberry fruits come off their receptacle when picked, if they're ripe. Yum yum!
Blackberry fruits don't come off their receptacle, but are still delicious.
Dewberries look like blackberries, but the plants trail along the ground rather than large arching stems. Still quite edible, tastier even that raspberries or blackberries.
So, how did I determine that the plant in the above picture is Black Raspberry (Rubus occidentalis)? I didn't! I just decided that every raspberry plant I see is Black Raspberry! :-0
I plan on calling every blackberry plant I see an Alleghany Blackberry (Rubus allegheniensis) and every dewberry a Northern Dewberry (Rubus flagellaris). I dare anyone to prove me wrong!