Specifically, mashing is the process of extracting soluble materials from the grains with water and enzymatically converting them into a form the yeast can use, while lautering refers to the separation of the liquid and solid portions of the finished mash. So mashing is an enzymatic/chemical process, and lautering is basically physical.
In big operations, a dedicated mash tun is essentially a second kettle designed to handle the thick mash. The lauter tun would be close to what we tend to use as a mash/lauter tun: insulated but not heated, with a false bottom for separation, and some kind of sparging aparatus.
The good thing is that, if you're doing full all-grain batches, you should already have a kettle large enough to act as a mash tun if you want to do temperature-step mashes. Then you can just dump it in the mash/lauter tun for separation.