Primary growth is the growth that allows the cell division to occur in the tips of the roots and stems. This is the reason for the formation of the primary tissues in the growing plants. Secondary growth pertains to the cell division that happens in the cambia that causes the stems and the roots to thicken.
For primary growth, the meristems that is responsible for the growth is the apical meristems which includes the root and stem apical meristems.
For the secondary growth, the lateral meristems play a big role in the formation of the plant laterally.