Extra as a prefix can mean apart from or outside of.
extradition
This site says it comes from the Latin extrā meaning outside of
However it can also mean 'more' or in addition to when used as a word.
Is one of the uses newer than the other?
Sources I've checked indicate that the word extra (not the prefix) is derived from "extraordinary". Obviously, that makes the prefix older. Since the very first time "extra" was used as a standalone word (apparently mid 1700s) it has meant "additional".
For example, the 1776 source The philosophy of rhetoric says:
I shall just mention another set of barbarisms which also comes under this class, and arises from the abbreviation of polysyllables by lopping off all the syllables except the first or the first and second. Instances of this are hyp for hypochondriac, rep for reputation, ult for ultimate, penult for penultimate, incog for incognito, hyper for hypercritic, extra for extraordinary. Happily all these affected terms have been denied the public suffrage. The humour of abbreviating now hardly subsists among us and requires no particular notice.
The sense of extraordinary that this refers to is now obsolete. It is defined in the OED as:
Additional to, over and above what is usual; = extra adj. Often following the noun; in which case the adjective cannot always be distinguished from the adverb. Obsolete.
"Extraordinary" in this sense dates back to at least the mid 1600s according to the OED.
This 1737 book, for example refers to both "charges extrary" and "charges extra.", where both are clearly abbreviations for extraordinary in this sense.
