[graph-tool] edge multiplicities vs edge covariates

Hello. As I understand, edge multiplicities is kind of number of edges between two nodes. And we can define it via 'eweight' attribute in BlockState. In some way (may be I'm wrong) if I differentiate initial edges by assigning to them different 'weights' via 'eweight', I will have also weighted graph model. What is the difference between edge covariates and edge multiplicities besides the generative model priors? Or I can consider them as a special simple case of more general 'edge covariates' of 'recs' attribute? Is there any discussion about this? Thank you. Valeriy