Sparse Matrix Matrix multiplication terminology (SpGEMM or SpMM?)

I have seen sparse matrix-matrix multiplication commonly referred to as SpGEMM, which means general/generalised sparse matrix-matrix multiplication. I've seen it once or twice (forgot where) as SpMM.

My question is, what is "general" referring to? The type of sparse matrix? Does there exist a non-general sparse matrix-matrix multiplication algorithm? All the routines/kernels I've come across are designed for sparse matrices which doesn't assume a structure, so isn't the word "general" a bit redundant? SpMM seems like a more fitting acronym.

I think this is a hold-over from the naming convention for the same routines in BLAS, where there are routines like DGEMM for double-precision, general matrix/matrix multiply, DSYMM for symmetric matrices, ZHEMM for complex Hermitian matrices, etc. The reason for the different routines is that, if you know the matrix is symmetric or Hermitian, you can use just the upper triangle of it to compute the result of a matrix multiply compared to the general case. Perhaps by saying SpGEMM they are implying that they also considered optimized routines for sparse symmetric matrices.