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On etymonline, it is stated that the prefix "dis" is related to the latin words "bis" and "duo."

Can it be correct to say that all three words are/were synonyms to each other?

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Related words/affixes share the same root, but this does not imply being synonyms.

duo, bis, dis- are not synonyms, they have different meanings and are not interchangeable.

PIE *dwóh₁, Latin duo is a numeral meaning "two".

PIE *dwís, Latin bis is an adverb meaning "twice, two times", so its grammatical usage is clearly different. Similarly in English you cannot replace "I ate two oranges." with "I ate twice oranges.". (Old Latin /dw/ (spelled <du> or <𐌃𐌖> in old alphabet) regularly changed to /b/. E.g. 𐌃𐌖𐌄𐌍𐌏𐌔 (duenos) -> duonos -> duonus -> bonus; *duellom -> duellum -> bellum)

Latin dis- prefix may come from PIE *dwís, but it has developed several different meanings in Latin (or Proto-Italic), one of them being "reversal, removal". difficilis ("difficult") is clearly not *bis facilis ("*twice easy").

Michiel de Vaan (2008, "Etymological Dictionary of Latin and the other Italic Languages"):

dis- 'away, apart' [pref.] (Andr.+)

Derivatives: dī- (in front of b,d,g,l,m,n,v,r; dismota SCBac.), dir- (in front of vowels), dif- (in front of f).

PIt. *dis- 'in two, apart'; *dus- 'bad' (in difficilis). It. cognates: possibly U. disleralinsust [3s.fut.pf.] '?will have gone wrong' < *dis-leis-?

PIE *dus 'into two > bad', *dui- 'two, into two'. IE cognates: Gr. διά 'in two, apart, through' [adv.], 'through' [prep.] < *δισ-α; also δα- in δαφοινός, esp. from animals, 'very red', δάσκιος 'very shady', developed from δια-, or Aeol. ζα-.

Borrowed into Gothic as the prefix dis- 'apart'. Lat. dis- seems to be cognate with Gr. διά < *δισ-α. Whereas διά can function both as a preverb and as a preposition, in Latin, dis- is only a preverb. In the older texts, it is nearly always prefixed to verbs, with the exception of the adj. difficilis. Exactly in this compound, dis- does not mean 'away, apart', but rather 'non-, opposite'. Therefore, it may well be that difficilis contains PIE *dus- 'apart; bad' (thus Wackernagel and Leumann 1977: 400), which is otherwise unattested in Latin. Yet Forssman 1992: 309 maintains that difficilis was built from dis + facilis on the example of similis : dissimilis. Even if difficilis does not directly continue *dus-, the restriction of dis- to (verbal) compounds would suggest that all of Latin dis- is a remake of *dus- by analogy with *dui- 'into two, apart'. Another possibility is a dissimilation *dwis- > *dis- in front of verbs starting in *w-, especially in the compounds dīvidere 'to divide' and dīvertere 'to divert'. Yet a separation of dis- from διά- is unattractive; and in Greek, δυσ- has remained alive as a prefix - but meaning 'bad'. Hence, Proto-Greek may have had all three forms: *dus- 'bad, *du̯i- 'two' and *dis-(a-) 'into two, apart'. Whereas *dus- developed from 'into two' to metaphorical 'bad', the novel form *dis- retained the literal meaning 'into two, apart'.

Sometimes related words may even be antonyms:

PIE *upó, Latin sub "under, below"

PIE *upér, Latin super "over, above"

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    This answer has very good information. I have two more questions: "Latin dis- prefix may come from PIE *dwís" : does that mean "it is possible that it came", or "although it came"? 2. Could you confirm or deny that all three morphemes are ultimately from the same Indo-European root?
    – Cerberus
    Commented Jun 21, 2023 at 19:08
  • @Cerberus: Dictionaries say that they are ultimately from the same root, however they present different paths for dis-. Wiktionary says that Latin dis- developed from Proto-Italic *dwis-, while Etymonline says that dis- prefix existed already in PIE: 「The Latin prefix is from PIE *dis- "apart, asunder" (source also of Old English te-, Old Saxon ti-, Old High German ze-, German zer-). The PIE root is a secondary form of *dwis-」. I am undecided about which path is more probable.
    – Arfrever
    Commented Jun 21, 2023 at 23:53
  • Old Latin initial /dw/ supposedly regularly changed to /b/, so *dwis -> bis is regular, while *dwis- -> dis- seems less regular...
    – Arfrever
    Commented Jun 21, 2023 at 23:58
  • Ok very interesting. Maybe add some of that to your answer?
    – Cerberus
    Commented Jun 22, 2023 at 0:56
  • Have you checked De Vaan? Pit. *dis- 'in two, apart'; *dus- 'bad' (in difficilis); PIE *dus 'into two > bad', *dui- 'two, into two'.
    – cmw
    Commented Jun 22, 2023 at 2:55

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