There are different cultivars, hybrids and species and they could all be growing side-by-side. I think you have at least 2 different species in your photos. In fact, I'm not sure that photos #1 and #2 are the same species. I am not going to attempt to identify your species, but lake a look at the number and arrangement of the leaflets on the compound leaf (photo 1 vs. 2), the robustness of the thorns (#7 is wicked), and the form or habit of the plant.
Blackberry plants can be very aggressive and invasive. Be sure to keep them corralled where you want them.