I think those are horse-chestnuts, different tree and not directly related to the American chestnut. We used to make little figures and animals out of the nuts and some matches in kindergarten.
Note that horse chestnuts (aka "buckeyes"), besides (as you say) being unrelated to standard chestnuts, are toxic. Just handling them is not a problem, but eating them is definitely bad news. Native Americans used to grind them up and use them to stun/kill fish.
Very bad news Indeed! Upvote for the PSA word of caution. I had a neighbor years ago who used just a few pieces of one as garnish on a soup. Made him horribly horribly sick; he survived without medical treatment, but attributes that mostly to the very tiny amounts he ingested.
