What is the difference between giving a table a name using #+TBLNAME and #+NAME in org-mode?
Org mode 8.2.10 is very old. If you can, you should upgrade. TBLNAME is deprecated (since version 8.3.4) : you should not use it any longer. It is still (in version 9.3) recognized for backward compatibility but it is likely to go away at some point. As for the link behavior mentioned in your answer, in recent versions of Org mode, [[a and b]] still results in the No match question, but [[c and d]] is a fully functioning link to the corresponding table.
Given two tables below only the one named using NAME can be
referenced in prose with a navigable link.
#+TBLNAME: a and b
| a | b |
| 1 | 2 |
#+NAME: c and d
| c | d |
| 1 | 2 |
The link [[c and d]] will not be navigable with C-c C-o while attempting
the same with the link [[a and b]] will result in the user being asked:
No match - create this as a new heading? (y or n)
But this is only part of the answer, there surely are more differences than this.
This is with org-mode 8.2.10 released with Emacs 25.2.2.
