First, note please that there is no "conjugation of würden":
wird, würd(e), werden and würden are all forms of the same verb, werden. The forms with ü are past subjunctive/Konjunktiv II forms which are derived from the past tense of werden which is er wurde/sie wurden. Although this subjunctive/Konjunktiv is derived from a past tense, its meaning is present.
The third person forms singular present of the verb werden are:
- indicative: er/sie/es wird
- (present subjunctive: er/sie/es werde)
- past subjunctive: er/sie/es würde
The form wird is pronounced with a final [t] sound because of the phenomenon known as Auslautverhärtung (terminal devoicing): In German, a final g sounds like a k, a final d like a t, a final b like a p, a final v like an f and a final s like an ß.
The forms werde and würde are pronounced with a [d] sound, because the d does not stand at the end of a syllable but is the first sound of the second syllable of the words.
In every-day speech, the form würde can be shortened to würd; sometimes this is marked with an apostrophe in written language: würd'. In this shortened form, the d is final again and is pronounced as a [t] sound.
My guess of why you perceive that wird and würd are pronounced with different d sounds is that the speaker was actually pronouncing the full form würde which has a [d] sound and somehow you missed the schwa sound which succeeds the [d].
I don't transcribe the full words in IPA because there are various possibilities to pronounce the combination vowel+r as in wird; instead I just wanted to focus on the pronunciation of d.