Some people would call a pile of something on the ground, a "structure". But in this context, the term is applied to a method of containing material for the purpose of actively composting it.

It does not matter whether you call it a structure - or a containment. I call it a structure, designed to be a containment. Most folks just call it a bin. Or a multiple-bin "set" - or a multi-compartment bin. Whatever.

There are a LOT of different kinds and types and styles - and I'm not going to attempt to provide information on all of them. If you want to do something different to contain your compost pile - I encourage you to experiment and follow your inclination. Point being - whatever works for you is the right way to do it.

I have my favorite containments for various reasons.

Thinking it through - deciding which material is least expensive for the purpose, easiest to construct, and whether or not you'll be collecting leachate tea. I strongly recommend collecting tea. Why? Read the section on Compost Tea - Leachate. Then you'll understand.

Any type of containment can be designed to efficiently collect the tea - runoff from watering the pile. As the water filters through the pile it picks up soluable plant nutrients, humic content (made by microbes) and some microbial life. Concentrating the tea by putting it back through the pile is a common practice. Point being that you want to consider how you're going to get the tea out of the barrel in the ground.

Check other links to learn details of each method.