I am shocked to say the least. I was outdoors last night weeding my flowerbeds and some shrubs and I noticed the strangest thing. Our blackberry plants had something I'd never in my life seen. It's also got another berry of a different species growing on the exact same plant. Can someone, anyone answer this question?
From what I can see, you appear to have only one bush, with blackberries in various stages of their life. A similar picture can be found here, along with some good information about the plant.
The berries are a yellowish white initially, and, as they ripen, turn first red, then black. The red berries are fine to eat but quite tart, whereas the mature fruit is much softer and more sweet.
There are a number of varieties which have different habits and fruiting schedules. I'm in Zone 6a and ours fully ripen in July, producing a large crop which turn our hands purple when we pick them! For us, that's part of the fun!
Edit: Thanks to the comments below, I learned that I provided some incorrect information about the effect of trimming on crop production. I've removed it! In case you're interested, a number of questions on the site offer thorough, accurate, instructions about how to grow and care for this plant. You can find them by searching the blackberry tag.