Export contacts with company seems to export all fields and even contacts that have company blank. SO why call it export contacts with company?
The other one, export items on screen, one might think it will only export what is shown on screen, but there can be several pages. From what I tested, it exports ALL contacts, and if you filter, then it exports whatever you filtered. So IMHO, a better label/name for option would be "Export all/filtered contacts".