The cooler type mash tuns in the homebrew stores or online are
exactly the same ones you find in the hardware stores.
Most LHBS sell the 10 gallon round ones. I prefer the rectangular ones, easier to stir, IMO. It takes only a a little handiness to mount the bulkhead, and check the seal for no leaks. You may save quite some $$ in the process.
Most cooler are made from food grade materials, so they are perfectly fine for use as a mash tun.
Stainless mash tuns need to be well insulated. Plastic coolers are fine as is, but in cold weather benefit from a blanket or sleeping bag cover.
Whether you need another 'HLT' cooler to store hot water depends on your process, I use a spare SS kettle, and heat my sparge water ~20' before the mash is done. I don't fly sparge, just batch sparge 2x with equal volumes. Easy peasy.
Here's the inside of my 52 qt Coleman Extreme mash tun,
manifold is shown upside down:
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