I will speak from the CS perspective, which I know.
If the type (regular, position, short) can say anything about the
quality or the importance of the paper's subject?
Unfortunately, it does. Although the short paper will still appear in the proceedings, it will have a maximum limit of usually 4 pages. Therefore most details will have to be omitted, due to the limited space. Also, in CS conferences short papers might be presented in a fast-forward fashion (1-2 minutes per paper) or together with the demo papers presentation and therefore they do not attract as much attention as the regular papers. In that case, during the demo / poster session people can come in to your "booth" and discuss about your paper (which is more informal but still a nice way to network).
The better way to take advantage of this situation (your paper was accepted after all, even as a short paper) is to make an extended version of this paper for submitting to a relevant journal, where you can reveal all the missing details from the proceedings short version, along with some additional extra material.