As you can see, there is indeed a story in the Talmud about a man called Jesus being burned in excrement. However, there are multiple stories in the Talmud in which a man called "Jesus" is mentioned, and not all stories perfectly line up together, and also not necessarily with the figure known as "the historical Jesus" (that they don't fit with the NT is of less consequence to Judaism). As such, there are those that believe that none of these stories refer to the same Jesus, like Rabbi Gil Student in the link that @TurkHill brought, or only somea couple of them. There are those that disagree, however, and say that at least some of the stories refer to the same Jesus, and perhaps even all of the stories can be connected together.
"...from the outset, before the accused is convicted, he does not go out. The Gemara raises a difficulty: But isn’t it taught in a baraita: On Passover Eve they hung the corpse of Jesus [the Nazarene]1 after they killed him by way of stoning. And a crier went out before him for forty days, publicly proclaiming: Jesus the Nazarene[the Nazarene]1 is going out to be stoned because he practiced sorcery, incited people to idol worship, and led the Jewish people astray. Anyone who knows of a reason to acquit him should come forward and teach it on his behalf. And the court did not find a reason to acquit him, and so they stoned him and hung his corpse on Passover eve."
Some have speculated parallels between these five and characters in the NT. Mattai is of course similar to Matthew. Netzer is similar to Nazarene (especially in Hebrew where they have the same root letters - נצר (Netzer)). Nakai might be similar to Nicodemus. Buni might be Barnabas. Toda might be Thaddeus.
But like with the story in Gittin, there are those that disagree with this interpretation. They may say that this might be a figurative tale in the Talmud, or perhaps it tells of another such sectarian with the same name, or perhaps by the time the Talmud was written, the name "Jesus" was a generic name for "bad man", or that Mary Magdalene wasn't even Jesus's mother, and so forth.
To conclude, the Talmud is vague in these stories. Whether on purpose or not - we can't be sure. Who these stories refer to - that's open to debate, much like how it's being debated to this day how much of the NT is believablereliable (in particular considering contradictions between the Gospels).