Structure Tensor vs. Hessian Matrix
The structure tensor consists of first derivatives of the image. If the first derivative is high in one particular direction (one large eigenvalue of the structure tensor), then you have an edge. It the first derivative is high in two directions (two large eigenvalues), then you have a corner.

The Hessian matrix consists of second derivatives. Think of the Laplacian. It is the trace of the Hessian, and it is a center-surround filter, which gives you a high absolute value for a bright blob surrounded by dark background or vice versa. That's why it is blob detector.