In the context of Org, a table typically means an Org-table. This type of table is what Org users use for formula (=*TBLFM*) and stuff. And it is these types of tables that you can do automatic align with TAB etc.
What you have with you is a table.el table. And table.el is a totally different library, and pre-dates Org-'s org-table.el library.
TLDR: What you have is a donkey (=table.el), and mistaking it for a horse(=org-table.el) you are doing horse stuff with the donkey. Horses and donkeys look alike, but they aren't the same.
+-----+-----+-----+ | | | | +-----+-----+-----+ | | | | +-----+-----+-----+ | | | | +-----+-----+-----+ * This is an `Org` table |---+---| | | | |---+---| | | | |---+---| | | | |---+---| * How to tell them apart? An `org`-table begins and ends with a `|` (= `pipe` character). A `table.el`-table may start and end with non-pipe characters.
Editing table.el table in `Org' mode
In an Org-mode, I entered M-x table-insert, and inserted the below table. Subsequently, I did C-c ' to edit the table.
From Packages that Org cooperates with (Hint: See towards the end of the page)
table.el by Takaaki Ota
Complex ASCII tables with automatic line wrapping, column- and row-spanning, and alignment can be created using the Emacs table package by Takaaki Ota. Org mode recognizes such tables and exports them properly. C-c ' to edit these tables in a special buffer, much like Org's code blocks. Because of interference with other Org mode functionality, Takaaki Ota tables cannot be edited directly in the Org buffer.
C-c ' (org-edit-special): Edit a table.el table. Works when point is in a table.el table.
C-c ~ (org-table-create-with-table.el): Insert a table.el table. If there is already a table at point, this command converts it between the table.el format and the Org mode format. See the documentation string of the command org-convert-table for the restrictions under which this is possible.
