It does get confusing. All the different shapes. Besides the different pieces Glen mentioned in the four pc. table set, Butter, sugar, creamer, spooner, you can add the celery, various sized compotes, trays, bowls salt dips (which went in conjuction with the celery vase, they were small dishes to hold salt and to dip your celery in.) Early American Pattern glass can be viewed much like a china service today. You would pick a favorite pattern and try to have as many pieces as you could so they all matched. Quite a feat when one considers that a given pattern might contain the celery vase, a dish for pickles and a seperate one for olives, an almond dish, cheese dish, jelly dish, mustard jar, toothpick holder, tumblers, goblets, etc.
Many a time I have had a dish and once having learned the pattern name, then tried to find out exactly what the dish was for. And to think at that time, no dishwashers OH MY!
Anyway for your enjoyment here is a selection of celery vases to show some of the variety you can find. http://tinypic.com/a9og8l.jpg