Older strawberry plants form a sort of "trunk" over time - they get a bit taller and show the remains of lots of earlier leaf growth. The new runners - should be much smaller plants, and you will often see the remains of the "runner" leading to the new plant. Many of the new plantlets will root OK even if detached from the mother plant but if possible you should try to root them before lifting them - just make sure they are touching the soil, or into a tiny pot of their own, held down with a bit of wire or such. Once they are big enough they can be cut free