We have multiple synonyms for full-form names and their abbreviations like item-response-theory and irt, or stochastic-gradient-descent and sgd. What should be the basic form: full length or abbreviated? The labels can be easily swapped.
Let the users decide in each case.
When creating synonyms, I have always chosen as the "target" (which is the name that will be displayed) the one most commonly used on the site.
The advantages of this procedure are evident: our tags reflect the values people naturally think of.
The disadvantage would be an apparent inconsistency--sometimes a target would be longer than its synonyms, sometimes shorter. But of what value would such a consistency be? I cannot see any.