Pretty much. English borrowed it from Latin because it's posh. And Latin borrowed it from Greek because it's posh. But at the end of the day it's in the same spirit as "the ABC", or Latin "abecedarius".
It is kind of the same suffix but the story is a mess.
That -ario and all words using it are reborrowed* from Latin. And originally it was two related suffixes, fulfilling two purposes:
masculine -arius, feminine -aria: transform noun into adjective. Like "a be ce de" (ABCD) into "abecedarius" (alphabetic).
neuter -arium: noun denoting a place for another noun. Like "dictio" (saying) into "dictionarium" (dictionary, or "where you store sayings")
Except that Latin allowed you to use an adjective as if it was a noun (Spanish still does it), so that "abecedarius" ended as a substantive again. And Spanish merged Latin masculine and neuter, further conflating both versions of the suffix.
*the inherited doublet is the -ero in llavero (place for keys) and herrero (related to iron - professions took the suffix and systematised the re-substantivisation).