i have planted a black berry shrub, it seems that there are tiny similar looking plants that are popping up about 1 or 2 meters away from the original plant.
so i am just wondering if that is the case?
Depends on the variety. Erect varieties do, trailing varieties do not. Sounds like yours is an erect/semi erect variety which will send out runners.
The wild blackberries around my yard most definitely do, as if I go a couple weeks without mowing the yard I will see blackberry vines cropping up upwards of a couple feet away from the vines proper.
I know mine would tip into the ground and root from there...don't recall them spreading like raspberries.