These little pieces of the past have a few different names: Open salts (still used by chefs/kitchens today), salt cellars, salt dish, salties and salt dips. They were used on elaborate and elegant settings when lots on the table setting was considered "in". They have been made open or closed. Plain or elaborate. (Some of my favorites: Viking ships, hens, etc.)
But realize that there are still places that make them because of their popularity. Interesting enough, there are places making the pressed glass ones using the original old molds....so they aren't considered reproductions...but most reputable firms will mark them a little differently to differentiate the timeline. PotteryBarn is starting to produce some in novel forms, etc.
The collecting of these pieces of history are so popular that there is now a convention, there are collectors clubs, etc.
This one site is remarkable! They have a section devoted to salt cellars by Makers even! :
INFORMATION ON PRESSED GLASS OPEN SALTS OF THE PAST 75 YEARS
http://opensalts.net/about_us.html