Rewording based on review comments

extensions/parquet/table/src/main/java/io/deephaven/parquet/table/ParquetTools.java

@@ -853,7 +853,7 @@ private static Collection<List<String>> indexedColumnNames(@NotNull final Table
      * Write out tables to disk. Data indexes to write are determined by those already present on the first source or
      * those provided through {@link ParquetInstructions.Builder#addIndexColumns}. If all source tables have the same
      * definition, this method will use the common definition for writing. Else, a definition must be provided through
-     * the write instructions.
+     * the {@code writeInstructions}.
      *
      * @param sources The tables to write
      * @param destinations The destination paths or URIs. Any non-existing directories in the paths provided are
@@ -879,7 +879,7 @@ public static void writeTables(
             for (int idx = 1; idx < sources.length; idx++) {
                 if (!firstDefinition.equals(sources[idx].getDefinition())) {
                     throw new IllegalArgumentException(
-                            "Table definitions must be provided when writing multiple tables " +
+                            "Table definition must be provided when writing multiple tables " +
                                     "with different definitions");
                 }
             }

extensions/parquet/table/src/test/java/io/deephaven/parquet/table/ParquetTableReadWriteTest.java

@@ -2014,7 +2014,7 @@ public void writeMultiTableExceptionTest() {
     }
 
     @Test
-    public void writeMultiTableDefintionTest() {
+    public void writeMultiTableDefinitionTest() {
         // Create an empty parent directory
         final File parentDir = new File(rootFile, "tempDir");
         parentDir.mkdir();

py/server/tests/test_parquet.py

@@ -746,13 +746,14 @@ def test_v2_pages_helper(dh_table):
         dh_table2 = self.get_table_with_array_data()
         test_v2_pages_helper(dh_table2)
 
-    def test_batch_write_without_definition(self):
+    def test_batch_write_definition_handling(self):
         table = empty_table(3).update(
             formulas=["x=i", "y=(double)(i/10.0)", "z=(double)(i*i)"]
         )
         table2 = empty_table(3).update(
             formulas=["x=i*2", "y=(double)(i/5.0)", "z=(double)(i*i*i)"]
         )
+        # Should succeed because both tables have the same definition
         batch_write([table, table2], ["X.parquet", "Y.parquet"])
         self.assert_table_equals(read("X.parquet"), table)
         self.assert_table_equals(read("Y.parquet"), table2)