Difference between under and below

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In your specific example, with a house on stilts, I think you could use either but I would have a preference for "below." "Under" suggests closer proximity than "below." If there was only a small place to crawl in beneath the house I would use "under." (I guess it might depend on the height of the stilts -- I'm not familiar with houses on stilts, so I don't know how much space there would typic

If the house were situated on a "side hill" (or hillside) "playing below the house" could be taken as "playing somewhat downhill from the house," while "under the house" would always mean "directly under." - A.

Edit. Sometimes hillside dwellings are partially on stilts, but I pictured the house in your example as being on level ground (for some reason).

It should be under or beneath the house-platform. Logically speaking, if the house is on stilts, the open space created by such model of house constructions also forms a part of the house itself. Moreover, if we just say beneath or under the house, without explaining what type of house it is, no body expect the writer will understand.

This is my view.

Generally speaking, below has to do with vertical levels. below is 'lower than'. under usually includes the idea of 'covering' as well as the idea of 'lower than'. under is 'covered by'.
I would choose under for your sentence, but below is also possible. When both are possible, choose under if you wish to emphasize that the location has som

A sloping (rather than vertical) example would apply to many of our larger mountains: above/below the tree line. - A. (Our respects and sympathies to all flatlanders.) Also, above/below sea level.

To people who live in hilly country, "the garage is below the house" could mean "beneath the house," or "downhill from the house." - A.

They are playing below the house.

under

I do know the differences b/w below and under:

below is used when one thing is not directly under another; and is used in measurements of tempreture and height;

under is preferred when sth is covered or hidden by what is over it; and also lesser than or younger than

- You can't drink if you are under 18.

They are playing below the apartment