I'm studying numerical methods to solve differential equations, but I don't understand the differences between "Backward differentiation formula" and "backward difference" (finite difference).
For example what formula it was applied here for the time derivatives ?
$w_\tau(\tau_m,\xi_i) \approx \begin{cases} (w^m_i-w^{m-1}_i)/k, & m=1,\\ (\frac{3}{2}w^m_i-2w^{m-1}_i+\frac{1}{2}w^{m-2}_i)/k, & m\geq2, \end{cases}$
Also, the acronym BDF stands for "backward differentiation formula" or for "backward finite difference" ?