# Spline interpolation versus polynomial interpolation

What is the difference, if any, between spline interpolation and piecewise polynomial interpolation?

Other people (like here) define a spline of degree $m$ to be a piecewise polynomial with $m-1$ continuous derivatives. So, with this definition, cubic splines (degree 3) would be $C_2$. These folks sometimes refer to less continuous piecewise polynomials as "subsplines" or "defective splines". In fact, a spline of degree $m$ that has a continuous $(m-k)$-th derivative is said to have defect $k$.