A key difference is that, in that case, the vaccine mandate was issued by the State, not the Federal government.I don't know if there is further law on this.
Additionally, the vaccine mandate in question was a state statute - i.e. duly enacted legislation, not a unilateral executive action. From the syllabus of the decision: "It is within the police power of a State to enact a compulsory vaccination law, and it is for the legislature, and not for the courts, to determine."