Looks like most of the images under handbag are purses, though there are a few others that would fall under other tags.
Posted under General
I did one wiki, while nanami did the other.
But unless there is a distinctive difference for Danbooru; they are alike to people.
Would a Handbag be a bag that is not carried on the shoulder? Or just smaller in size compared to a Purse? Basically taking the title "hand" literally.
I don't think there is a difference. On Wikipedia handbag is an alias for purse.
A purse that is carried just in the hands is called a clutch or clutch bag. As for size, the size of the bags in the images tagged handbag from what I saw seemed to widely vary, so I don't think there was any real specifics there, at least for taggers. There are some in there that looked more like sports bags or duffel bags.