Detail ordering-dependent behavior in documentation

refs idaholab#17710

framework/doc/content/source/meshgenerators/RenameBlockGenerator.md

@@ -6,7 +6,7 @@
 
 When using the `RenameBlockGenerator` to change block names, the result is independent of ordering.
 
-The following will change the name for the block "meaningless" to "inside" and will set the name for block "5" to "outside":
+The following will change the name for the block `meaningless` to `inside` and will set the name for block `5` to `outside`:
 
 ```
 [rename]
@@ -19,43 +19,66 @@ The following will change the name for the block "meaningless" to "inside" and w
 
 ## Merging Blocks
 
-When using the `RenameBlockGenerator` to merge blocks, the result is not necessarily independent of ordering.
+The `RenameBlockGenerator` can be used to merge blocks together. The result is independent of ordering when [!param](/Mesh/RenameBlockGenerator/new_block) contains only block IDs. When [!param](/Mesh/RenameBlockGenerator/new_block) contains block names, the result is not necessarily independent of ordering.
 
-For example, take the following:
+The following will result in the merging of the elements in blocks `1`, `2`, and `3` into block `0`:
 
 ```
 [merge]
   type = RenameBlockGenerator
   input = some_mesh
-  old_block = '0 1 2 3'
-  new_block = '0_and_1 0_and_1 2_and_3 2_and_3'
+  old_block = '1 2 3'
+  new_block = '0 0 0'
 []
 ```
 
-The above will result in two blocks:
+As discussed previously, when providing names in [!param](/Mesh/RenameBlockGenerator/new_block), the result may be ordering-dependent. If a name is provided in [!param](/Mesh/RenameBlockGenerator/new_block) that does not already exist in the mesh, it will take the ID of the first rename.
 
-- Block "0_and_1" with ID "0" that contains the elements from the original blocks "0" and "1".
-- Block "2_and_3" with ID "2" that contains the elements from the original blocks "2" and "3".
+Take the following examples (assuming that the block `some_block` does not exist yet):
 
-Take the first execution, "0" to "0_and_1". The `RenameBlockGenerator` will use the original block ID, which is "0". The second execution "1" to "0_and_1" will use the new ID associated with "0_and_1", which is "0", and merge "1" into it. The result is similar for the third and fourth executions.
+```
+[mergename0]
+  type = RenameBlockGenerator
+  input = some_mesh
+  old_block = '0 1'
+  new_block = 'some_block some_block'
+[]
+```
 
-!alert! tip title=The use of ID is order independent
-The order dependent behavior only exists when the new block provided is a name. Take the following instead:
+```
+[mergename1]
+  type = RenameBlockGenerator
+  input = some_mesh
+  old_block = '1 0'
+  new_block = 'some_block some_block'
+[]
+```
+
+The result of each will be a block named `some_block` that contains elements that were in blocks `0` and `1`. However, because the block `some_block` takes the ID of the first rename execution, the ID of `some_block` will be `0` in the case of the generator `mergename0` and `1` in the case of the generator `mergename1`.
+
+In the case of providing [!param](/Mesh/RenameBlockGenerator/new_block) by ID, the following examples (assuming that the block `2` does not exist yet) will have the same result:
 
 ```
-[merge]
+[mergeblock0]
+  type = RenameBlockGenerator
+  input = some_mesh
+  old_block = '0 1'
+  new_block = '2 2'
+[]
+```
+
+```
+[mergeblock1]
   type = RenameBlockGenerator
   input = some_mesh
-  old_block = '0 1 2 3'
-  new_block = '0 0 4 4'
+  old_block = '1 0'
+  new_block = '2 2'
 []
 ```
 
-The result is:
+That is, a block will be created with the ID `2` that contains the elements previously in blocks `0` and `1`.
 
-- Block "0" that contains the elements from original blocks "0" and "1".
-- Block "4" that contains the elements from original blocks "2" and "3".
-!alert-end!
+In summary, the possibility of ordering-dependent results with the `RenameBlockGenerator` depends on whether or not name(s) are provided in [!param](/Mesh/RenameBlockGenerator/new_block) and said name(s) do not exist yet.
 
 !syntax parameters /Mesh/RenameBlockGenerator