The confusion is caused by the fact that some of the books of the Bible and the apocrypha (those which do not belong in the Catholic Bible) have changed names over the last few centuries. You have put your finger on the most confusing name change there has been. Read carefully, because this is tricky.
There have been four books associated with the prophet Ezra (also spelled Esdras). In some circles these became known as 1, 2, 3, and 4 Esdras. In other circles, the first two of these (1 and 2 Esdras) became known as Ezra and Nehemiah, while the second two (3 and 4 Esdras) became known as 1 and 2 Esdras.
The first two of the four books belong in the Bible and are accepted by both Catholics and Protestants as canonical. In older Catholic Bibles they were called 1 and 2 Esdras, but now they are more commonly called Ezra and Nehemiah. The second two of the four books (sometimes known as 3 and 4 Esdras, sometimes known as 1 and 2 Esdras) do not belong in the Bible at all and are not accepted by either Catholics or Protestants.
When we said that the Church councils did not accept 1 and 2 Esdras, we were using the modern system of book names and were referring to the two formerly known as 3 and 4 Esdras.
One final note to the confusion: While 3 and 4 Esdras are not accepted by Catholics or Protestants, some Eastern Orthodox accept one or the other of them.