The nomenclature of the various Ezras can be confusing. This is because the Hebrew Bible, the Septuagint, and the Vulgate all use similar names in different ways to refer to the same set of texts.
From the Hebrew Bible point of view
Ezra is 2 Esdras 1-10 in the Septuagint and 1 Ezra in the Vulgate.
Nehemiah is 2 Esdras 11-23 in the Septuagint and 2 Ezra in the Vulgate.
From the Septuagint point of view
1 Esdras is 3 Ezra in the Vulgate.
2 Esdras 1-10 is Ezra in the Hebrew Bible and 1 Ezra in the Vulgate.
2 Esdras 11-23 is Nehemiah in the Hebrew Bible and 2 Ezra in the Vulgate.
From the Vulgate point of view
1 Ezra is Ezra in the Hebrew Bible and 2 Esdras 1-10 in the Septuagint.
2 Ezra is Nehemiah in the Hebrew Bible and 2 Esdras 11-12 in the Septuagint.
3 Ezra is 1 Esdras in the Septuagint.
Working among the Bible versions in Ezra is thus particularly confusing.