Are "traitor" and "trader" pronounced the same?

Solution 1:

The allophones of /t/ in English are [tʰ], [t], [ɾ], and [ʔ]. Which of those you get in any particular word and speaker depends on many, many factors.

Both trader and traitor alike are indeed pronounced [ˈtʰɹeɪɾɚ] by most North Americans, particularly in casual or quick speech.

Intervocalic /t/ almost always reduces to a single flap [ɾ] there. That’s why ladder and latter are homophonic, although kitten and kiddin’ are not. Indeed, kitten may become just [ˈkʰɪʔn̩] (sometimes written [ˈkʰɪʔən]) , often enough.

In contrast, intervocalic /t/ does not reduce to a flap in RP; it can sometimes do so in other British dialects, though. So RP would make traitor into [ˈtʰɹeɪtə] instead, with a linking [ɹ] at the end as needed for liaison only.

In Scots English you might find [ˈtɾeɪtʰɚ] (sometimes written [ˈtɾeɪtʰəɹ]), though, with now the initial ‹r› converted into a flap instead of the ‹t›. Just depends on the speaker.

See here for innumerably many other fascinating details and distinctions. In particular, see for example better and daughter. (Just don’t take too seriously the uptalking teenaged boy they got for the General American; that sort of high-tone rising is not commonly heard in older speakers. It has a very “valley girl” sound to it.)

Solution 2:

In American (but not British) English, /t/ and /d/ following a stressed vowel and preceding an unstressed one are normally neutralized to a flap [ɾ] sound.

There are a lot of pairs that are neutralized this way; the standard example is writer ~ rider. However, that doesn't leave the pair indistinguishable, since English native speakers often lengthen stressed vowels before voiced consonants, and that vowel length is retained even after neutralization, so Americans pronounce them as ['rəiɾər] and ['ra:iɾər], respectively. (In that case, /ai/ is reduced to [əi] before voiceless consonants anyway, like wide and white, but that's only true of /ai/ -- and in Canada, /aw/)

In the case of traitor and trader, that would be ['tʰreɾər] and ['tʰre:ɾər], respectively, in the U.S. and Canada. English doesn't have phonemic vowel length, but some vowels are held longer than others anyway; listen for them and you'll hear them.