IPA contains diacritics for indicating voiceless (/x̥/) and voiced (/x̬/) sounds. There are also different symbols for many voiced/voiceless pairs, e.g. /d/ and /t/ or /g/ and /k/.
Is there a difference between the sounds /d/ and /t̬/?
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I usually only ever see the voiceless diacritic used on segments for which voicelessness is highly marked, like the devoicing that occurs in /Cr/ clusters in English. [tr̥æp]. Usually, a liquid like r is voiced, but in this particular instance, it is remarkably voiceless.
As for whether there's a difference between d and t̬ , I think the answer is that IPA transcription is frequently more of an interpretive exercise than a science.
The real question to ask is if you were presented with some audio from a language that contains what sounds like a voiced, alveolar stop, which symbol would you use? I think many times it depends on what else you know about the language, or word you're transcribing. What if you also knew that this language had no voiced stops, and that in this particular piece of audio, it sounds voiced because it's between two vowels? In that case, you might be tempted to use [t̬ ], to reflect your beliefs about the phonemic system. Or, to take the example from Theta30's comment, you might know that a word had an underlying /t/, but it gets voiced or flapped in some contexts, so you add a voicing diacritic to reflect that.
On the other hand, if you also knew the language in question does have voiced stops, or that this particular word does have underlying /d/, you might choose [d] to reflect those beliefs.