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: 
The Item Modification Stations are now required to add Augments to your gear. When you buy an Augmentation Kit you have to take it to one of the stations and pay to apply it to your gear, giving you an augment slot. You can then use the station to add an augment or simply modify the gear as normal with Ctrl + Right Click. (They still allow you to adjust other mods with the stations.)

Augments are exactly the same as other mods, they add extra stats. All equippable items can be augmented.
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.