Aion and aionios are the same word. They mean the same thing. Aion is the noun and aionios is its adjective form. Aionios is just an inflection of aion. English also uses inflections. For instance, happy is the noun happily is the adjective. Both have the same meaning, they are just used differently in a sentence.
Sorry, but I'll the word of the concordance over yours.
αἰώνιος
aiōnios
ahee-o'-nee-os
From G165; perpetual (also used of past time, or past and future as well): - eternal, for ever, everlasting, world (began).
Total KJV occurrences: 71
aiōn
ahee-ohn'
From the same as G104; properly an age; by extension perpetuity (also past); by implication the world; specifically (Jewish) a Messianic period (present or future): - age, course, eternal, (for) ever (-more), [n-]ever, (beginning of the, while the) world (began, without end). Compare G5550.
Total KJV occurrences: 128
If you don't like Strong's, I also have a Thayers,
αἰών
aiōn
Thayer Definition:
1) for ever, an unbroken age, perpetuity of time, eternity
2) the worlds, universe
3) period of time, age
Part of Speech: noun masculine
A Related Word by Thayer’s/Strong’s Number: from the same as G104
αἰώνιος
aiōnios
Thayer Definition:
1) without beginning and end, that which always has been and always will be
2) without beginning
3) without end, never to cease, everlasting
Part of Speech: adjective
A Related Word by Thayer’s/Strong’s Number: from G165
I also have a NASEC lexicon
αἰώνιος
aiōnios; from G165; agelong, eternal: — eternal (66), eternity (1), forever (1).
I also have Greek to English Lexicons by Frederic Danker. Unfortunately I don't have it in electronic form, so I can't copy and paste here.
G166 - aiōnios - Strong's Greek Lexicon (kjv)
G166 - αἰώνιος aiṓnios, ahee-o'-nee-os; from ; perpetual (also used of past time, or past and future as well):—eternal, for ever, everlasting, world (began).
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