What is a text box generator?
Can I use this for ASCII art?
How do I copy the generated box?
The free ASCIIflow website will let you draw text boxes, text, lines, arrows, freeform lines, erase, import, export, and even undo/redo. What else would one need?
Here is my wonderful creation using this tool:
+-------------------------------+
| |
| My first ASCII box |
| |
+---------+---------------------+
|
|
|
| My first ever ASCII arrow
|
|
|
+---------v----------------------+
| |
| My second ASCII box |
+--------------------------------+
It is possible to draw such pictures using tools dating back 30 years, namely pic which is part of the troff command suite. These days gnu's groff package will contain the pic command. The link shows a picture of some typical PostScript output, but using nroff or the appropriate options you will get an ascii-art version. See the user manual (pdf) from 1991 for examples.
The tables in your example are probably produced by this same command suite, using just tbl which produces tables from simple lists.
For a gui version, you can use artist-mode in emacs to draw boxes and arrowed lines etc, using the mouse or keyboard. See youtube video demo.