They're not the same.
Short term leave is issued on an availability basis - it shows as AL on the roster - if you have leave in the bank then it will be given if they have the resources (enough pilot cover)
Emergency leave - shown as EL on a roster - is issued depending on your circumstance and although also comes from your leave bank, if you have none then it will leave you with a negative amount and taken from next years 42 days. Even if they don't have enough cover you will get the leave for things like death in the family.
Alan