No, metanoeo is the verb (action), and metanoia is the noun. Kind of like believe and faith. Verb and noun. They aren't different.
I urge you to check 2 Pet 3:9 on biblehub.com and see for yourself what "repentance" means.
Strong's Concordance
metanoia:
change of mind, repentance
Original Word: μετάνοια, ας, ἡ
Part of Speech: Noun, Feminine
Transliteration: metanoia
Phonetic Spelling: (met-an'-oy-ah)
Definition:
change of mind, repentance
Usage: repentance,
a change of mind, change in the inner man.
HELPS Word-studies
Cognate: 3341 metánoia – literally,
"a change of mind" ("
after-
thought");
repentance.
See 3340 /metanoeō ("repent").
Like a verb and a noun.
We are saved by faith in Christ. And that requires changing one's mind about a number of things.
1. must realize (change the mind) about one's own sinfulness.
2. " " " " " " " need for salvation.
3. " " " " " that Christ is God.
4. " " " " " that Christ dief for your sins.
5. " " " " " you must trust Him to save you.