anonymous seem to be right about two JTS-es. Wiki says
“Jewish Theological Seminary Association” was founded with Morais as its President in 1886 as an Orthodox institution to combat the hegemony of the Reform movement.[5] The school was hosted by Rabbi Henry Pereira Mendes’ Congregation Shearith Israel, a sister synagogue to Mikveh Israel.
In October 1901, a new organization was projected entitled the “Jewish Theological Seminary of America,” with which the association was invited to incorporate.
R Morais was already niftar and Rev Mendes stepped down either in 1901 or 1902.
About 100 days after Schechter’s appointment, the Agudath Harabbonim formed, principally in protest, and declared that they would not accept any new ordinations from JTS, though previous recipients were still welcome.
Anyway, given that Schehter came from a Chabad family, we are firmly back to the topic, and let Chabadnikim explain how one of their own founded JTS-2.