This is quite an arcane subject. However, the short answer is that what determines when a
stater is termed that, rather than a
didrachm, is little more than popular usage.
The original
stater was the primary denomination of the early coinage (after the cessation of usage of naturally occurring
electrum) in parts of
Asia Minor and was based on a fixed
weight of gold.
Stater in this sense is a numismatic term for the primary denomination off which all other denominations are keyed e.g
hemistater being half a
stater.
Coinage when initially struck in gold
poor Greece was based on a primary denomination in silver (valued at roughly one tenth that of gold by
weight). This occurred in
Aegina with the primary denomination being a coin of 12.2 gm of silver. This came to be called a
stater by numismatists, though what the ancient
Greeks called it is unknown to me, and I suspect everyone else.
This name sticks, although technically it could equally well be called a
didrachm as shown in the simple summary of
weight standards below from Morkholm's publication
Early Hellenistic Coinage. The key point of this table is that the stater/didrachm is a primary denomination in all Greek
weight systems, albeit with a different
weight of silver being the basis of each system.
So far so
good? Then the Athenians moved to a light stater/didrachm based system of ca. 8.5 gm silver for the primary denomination. This is called a
didrachm, rather than a
stater by numismatists for no other reason that the Greek equivalent of the word
drachm was what half a
didrachm (or
hemistater) was called in
Athens (or so I am led to believe). Thus we call an Attic
weight standard tetradrachm exactly that rather than a
Distater.
Now to add to the confusion a
stater as called by numismatists in the Attic
Weight system reserved for a denomination in gold with a base unit
weight of 8.6 gms.
Confused? Most people (including me) are by this stage and we have yet to move on to the Phoenician
Shekel, Persian Daric and
Siglos, or the
Litra of
Sicily, which was based on a primary unit in bronze.
Morkolm's
Early Hellenistic Coinage has a nice summary of the evolution of these
weight systems and a more expansive explanation can be found in the Preface to any of the volumes of Oliver Hoover's
The Handbook of Greek Coinage.At the bottom of this
thread is a more comprehensive overview of
weight standards
https://www.forumancientcoins.com/board/index.php?topic=10182.0Some nice pictures and a very high level summary of denominations can be found here
http://www.classicalcoins.com/denominations.htmlPS This is why we have some coins such as the Babylonian Baal/Lion coins called variously
lion staters or tetradrachms, sometimes simultaneously in the one publication!
Similarly you will see Carthaginian coins described as 1 1/2 Shekels or Tridrachms... not much sense in either case as we have no idea what they were really called. The Carthaginians being of Phoenician extraction, I suspect they were originally struck by the Carthaginians with a lower silver to gold value than the Phoenician
Shekel, reflecting
Carthage's original gold based economy, prominence and wealth, and were called a
shekel by the Carthaginians despite being 50% heavier that the Phoenician silver
shekel.