Plain yogurt is strictly defined by the FDA. It's when you have flavored versions that the rules get loose.

For example this contains only milk, cream, bacteria: https://www.traderjoes.com/home/products/pdp/plain-whole-mil...

This is basically sugary milk with thickeners added to make it vaguely like yogurt: https://www.yoplait.com/products/original-single-serve-straw...