As you know or might not know, in Japanese there are many different counters used to count different things. It’s not like it is in English. Unfortunately, Koichi doesn’t state this anywhere in the beginning of Textfugu, which leads to mass confusion from people who have little or no prior knowledge of Japanese. Perhaps he will state this in a future update.
Fortunately, he did write a guide on Tofugu about the most common counters: http://www.tofugu.com/guides/japanese-counters-guide/
一つ (ひとつ) = one thing, 二つ (ふたつ) = two things, 三つ (みっつ) = three things, etc. This is the general counter to count “things”. As he says in the guide, you shouldn’t rely on this too much and only use it for things that don’t have counters or aren’t specified.
一人 (ひとり) = one person, 二人 (ふたり) = two people, 三人 (さんにん) = three people, etc. This is the counter for counting people. It usually ends in にん but the first two are different.