Nitpicking title: 'Town' vs. 'City', bugs me as a former CO resident. Ft. Collins is huge (~170k people compared to most CO towns which are 400-10k ppl). The title sort of leads you to believe it was a folksy, rural community effort. In reality Intel, AMD, Broadcom and a major State University are located there and that probably helped the effort substantially. https://en.wikipedia.org/wiki/Fort_Collins,_Colorado#Maj…
I looked into this, and Ft. Collins is a "Home Rule Municipality" under state law, meaning it can name itself either a town or city. It seems to have chosen to be a city, so you're right. Around the world, it seems that there's one consistent criterion for something being a city: it must have self-rule and a certain amount of government structure. Some places (notably not the US) have population requirements, but tho…
What do you mean by self-rule? Singapore is autonomous, but that's definitely not the norm for cities. Almost all of them belong to larger states.
No US city has self-rule even at the level below the federal government. Washington, DC comes closest, but it is technically ruled directly by the federal government (in a manner that is not true for cities that belong to states). China has four "province-level" cities, but is generally accepted to have many more than four cities.