Difference between the Hot Liquor Tank, Mash Lauter Tun and Boil Kettle

Is there any physical difference between the Hot Liquor Tank, Mash Lauter Tun and Boil Kettle?  I know that the mash tun should have a false bottom, but beyond that, this is still new. Before investing a significant amount of money, would I need to purchase three different vessels, or could I get by with two? Currently I only own a 8.5 gallon boil kettle w/o valves or thermometer. I am just trying to best inform myself before I blow a bunch of money.

Short answer no. truthfully you can get by just with the kettle and some buckets. It's a huge pain and there are a number of headaches I won't even get into but I've done it with only a kettle and buckets and still made good beer. I invest in one item at a time normally weather its an upgrade or flat out new equipment. Really you just need to figure what it's worth to you. My advise by a cooler for a mash tun and some valves for your kettle and tun. That way your basics are covered. Cheers

I was in your position a few years ago. Simplest way to go is BIAB, using the pot you have now. Probably only make  say 3-4 gallon batch since all your grain and water are in there at once. Beersmith can confirm how big of a batch you can make. That way you can judge for yourself if any upgrade investments are worth it. I made BIAB once after making extract batches for years. I loved the all grain outcome so much; and right away bought a new bigger S.S. pot on sale and made my own kettles by purchasing and installing valves, thermometers, bazooka screens, etc. If you are mechanically inclined it's very easy. If not find a buddy who is, in return for some homebrew. Otherwise you can lay out big bucks for premade brew kettles. Cheers