Tsung-Wen,
Actually, the two forms are equivalent. The LAMMPS doc page shows the original Tersoff form, written as a full double sum over i and j. The TEA form replaces the full double sum with the i>j half sum. This restriction requires combining pairs of b_{ji} and b_{ij} terms. The TEA form is not as computationally convenient as the original Tersoff, but both forms are mathematically equivalent. Same goes for the tersoff/zbl pair style.
Aidan