Is one American English and the other British English?I've seen both also. I don't think there's any difference, and the institution administering the test can call it whichever one it likes. (For the record, I like "admissions" better, but that's just personal preference.)
Actually, I disagree with you, Keith: it's not an adjective for me, it's a noun modifying another noun - which opens up the possibility of a plural inflection.There are two reasons for using the singular.
1) It's an adjective; English adjectives have no plural.
2) You take the exam to gain (an) admission.