Masechet Sanhedrin, Perek Dalet, and Mishnah Bet will list the 9th and 10th differences: a case in which we're going to put somebody to death if he is found guilty is different from other types of regular cases.
The Mishnah says: “In cases of purity and impurity and other types of Issurin, of prohibitions, that are going to be talked about by the Sanhedrin, when the Sanhedrin is dealing with these matters, we start with the greatest judge.” He gives his opinion first. It would be considered disrespectful if one of the lesser judges, one of the judges who was on a lower level than that wise judge, spoke. We don't want to disrespect the wise judge, so we have him speak first.
But when dealing with cases where somebody may be put to death, we start from the side. As we'll continue to discuss in this Mishnah or in this Perek, they would have a semicircle of Dayanim (judges). The people on the side of the semicircle were considered to be the lower-level judges, and they would give their opinions first, before the greater judge. Because the Halacha (Jewish law) is that, when dealing with murder cases or cases where we would put somebody to death, once the greatest judge has expressed his opinion, the lesser judge would not be allowed to contradict him. So we start with the lower-level judge and work our way up to the higher-level judge.
Last difference. Everybody is qualified to judge a case of money and other types of similar cases, even the son of a convert and the product of a forbidden marriage, which is a mamzer. If two people who are not allowed to get married marry and have a child, that child is a mamzer. These types of people, if they have the right knowledge, would be allowed to judge these types of cases of money and other such matters.
But not everybody is qualified to be a judge on a case where we may put somebody to death. Only Kohanim (priests), Leviim (Levites), and Yisraelim (Israelites) who have pure lineage and would be able to marry the daughter of a Kohen. Other types of people who have a psul, who have a problem with their lineage, would be unable to judge this type of case of capital punishment.