If abnormal means "not normal", then why are the original, native people called "aboriginal" people?

aboriginal means:

a person, animal, or plant that has been in a country or region from earliest times. an aboriginal inhabitant of Australia.

mid 19th century: back-formation from the 16th-century plural aborigines ‘original inhabitants’ (in classical times referring to those of Italy and Greece), from the Latin phrase ab origine ‘from the beginning.’

–Google

The Latin prefix ab means "of, from, by, since". –Wiktionary

But it can also mean away from. –Wiki

Since Mazura's answer explains the aptness of the word aboriginal as a term for "original inhabitants," my answer focuses on a somewhat different question posed (albeit obliquely) in the title to the posted question: Why does the 'ab-' in 'abnormal' seem to mean "not [normal]' while the 'ab-' in 'aboriginal' seems to mean very nearly the opposite ('original', not 'not original')?

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The 'ab-' in 'aboriginal'

Michael Quinion, Ologies and Isms: A Dictionary of Word Beginnings and Endings (2002) has an interesting but not entirely clarifying entry for the prefix ab-:

ab- Also abs-, Off, away, or from. {Latin ab-, with the same meaning.}

This is not a living prefix; words containing it ere imported into the language from Latin, often with a figurative sense.

some examples are abdicate (dicare, to declare), to renounce the throne; aborigine (ab origine, from the beginning), an inhabitant of a place from earliest times; abort, to terminate a pregnancy (oriri, be born); and abuse, to use something improperly (abuti, to misuse, from uti, to use).

Abs- is used before c and t, as in abscess (cedere, to go), abscond (concere, to hide or stow), and abstruse (trudere, to push).

As Mazura's answer suggests, ab- can be understood in a connecting cause-and-effect sense (indicating that something is traceable to something else) or in a distancing sense (indicating that something has changed or moved away from something else).

Thus, for example, abhor—"to regard with extreme repugnance : LOATHE," according to Merriam-Webster's Eleventh Collegiate Dictionary)—arises from ab- + horrēre ("to shudder"). Interpreted literally, the Latin combination starts with the shudder and extracts the feeling of loathing from that; the one comes from the other. Likewise, absurd—"ridiculously unreasonable, unsound, or incongruous," according to the Eleventh Collegiate—arises from ab- + surdus ("deaf, stupid"): the illogic or foolishness comes out of the underlying stupidity.

On the other hand, the distancing sense of ab- predominates in words such as abaxial ("situated out of or or directed away from the axis"), abduct (ab- + ducere, "to lead") and ablution (ultimately from ab- + lavere—"to wash"—with the more emphatic sense of washing away).

In having these dual senses, ab- is not all that different from the English word from, which can be used literally or figuratively in a connecting cause-and-effect sense (as in "from little acorns") or in a distancing spatial sense ("from far Cathay"). It's just that native English speakers grew up with from and so tend to take its protean applicability for granted.

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The 'ab-' in 'abnormal'

Having said all that, I should note that etymologically abnormal doesn't consist of a straightforward combination of a Latin ab- prefix and a Latin root word. To the contrary, according to the Eleventh Collegiate, it has this derivation:

{alter[ation] of F anormal, fr. ML anormalis, fr. L. a- + LL normalis normal} (ca. 1836)

That is, the ab- in abnormal comes not from Latin ab- (meaning "of, away, or from") but from Latin (and before that, Greek) a- (meaning "not"), through a French medial term that likewise used a- as the prefix. The alteration from a- to ab- in this case is, in a word, abnormal.

Glynnis Chantrell, The Oxford Dictionary of Word Histories (2002) has this entry for abnormal:

abnormal {mid 19th century} This spelling is an alteration, by association with Latin abnormis 'monstrous', of the 16th-century English word anormal. The latter was an adaption of a French variant of anomal, the variant being influenced by Latin norma 'rule, pattern'. The word in English was taken to mean 'away from the norm'. The root is Greek anōmalos 'not even, irregular'.

And Ernest Weekley, An Etymological Dictionary of Modern English (1921) offers this entry for abnormal, quoting from the New English Dictionary (NED), better known today as the Oxford English Dictionary:

abnormal. "Few words show such a series of pseudo-etymological perversions; G[reek] ανωμαλος, L[atin] anomalus, having been altered in Late L[atin], fter norma, to anormalis, whence F[rench] anormal and E[nglish] anormal, the latter refrrred to L[atin] abnormis and altered to abnormal. It has displaced the earlier abnormous" (NED).

As for abnormis, Chantrell's assignment of the meaning "monstrous" to that word seems a bit tendentious. The term seems to have originated with the more prosaic meaning "out of square" and then more evolved more generally to mean "irregular" or "away from the rule." Cassell's Latin Dictionary (1968) offers this entry for abnormis:

abnormis irregular, unconventional: abnormis sapiens, a philosopher of no particular school, Hor[ace]

and this entry for norma:

norma a carpenter's square for measuring right angles: Pli[y]. TRANSF[ERRED,] any rule, standard

So there is an abnormis in Latin—but that word only indirectly influenced the English pronunciation and spelling of abnormal, which directly evolved from the French word anormal—and did so at a surprisingly recent date.

As noted above, the Eleventh Collegiate reports a first occurrence date of 1836 for abnormal. However, a Google Books search finds numerous earlier instances of the term—in a summary of a case study from Silesia noted in the October 1818 New-England Journal of Medicine and Surgery (published in Boston but drawn from the Continental Medical Repertory for March 1817); in an article on epilepsy in the January 1826 issue of The Medico-chirurgical Review and Journal of Medical Science (published in London); in an article on "the white elephant of Siam" in the October 1828 issue of The Farrier and Naturalist (also published in London); in multiple articles in the February through November 1830 issues of The Transylvania [Kentucky] Journal of Medicine and the Associate Sciences; multiple times in John Eberle, A Treatise on the Practice of Medicine, volume 2 (published in Philadelphia in 1830), in an article on fossil Megalonyx bones found in a cave in Kentucky, read on March 8, 1831 and published in Journal of the Academy of Natural Sciences of Philadelphia; and multiple times in an 1831 translation of Adolph Otto, A Compendium of Human & Comparative Pathological Anatomy. Still, I had not expected to find that abnormal dates back only to the early 1800s.