Question: It seems that any modification you can do to a weapon on the Item Modification Table can also be done from Inventory.

Why are there so many tables and why would I want to use them?

Answer: 
UPDATE: New features to the game including customizing augments. This feature requires the Item Modification Tables now. See Matthew Read's answer. The original answer that applies to the game as it was originally released, is still included here:

ORIGINAL: 

It is a remnant from earlier item modification game mechanics Bioware was trying. 

Currently the Item Modification Table has no special purpose. You can modify an already-modifiable item by `Ctrl + Right Mouse Click`-ing the item in your character or inventory window. You can still use the table to start this process if you want, but you don't need to.

EDIT: One on each starter planet is also used as the target of a "how to use item mods" intro quest.
Here's what I have noticed: For example, I have 2 guns in my inventory that are non-mod. However, they pop up when I use the modification stations, allowing me to add and extract modifications there when I was unable to in my inventory.