PCA is a statistical model -- the simplest factor model there is. It deals with variances and covariances in datasets. It returns a transformed dataset that's l

PCA is a statistical model -- the simplest factor model there is. It deals with variances and covariances in datasets. It returns a transformed dataset that's linearly related to the original one but has the first variable with the highest variance and so on. SVD is a matrix decomposition. It generalizes the idea of representing a linear transformation (with same dimensions in domain and codomain) in the basis of its eigenvalues, which gives a diagonal matrix representation and a formula like A = V'DV. SVD is like this, but for rectangular matrices. So you have two matrices to diagonalize: A = U'DV. That SVD even performs PCA as noted in the algorithms is a theorem, albeit simple one usually given as an exercise. But hey, even OLS regression can be programmed with SVD if you want to.