The definition has changed throughout the years, hopefully we can all at least agree on that. Some early "shakes" had no milk whatsoever! I didn't know this either, but apparently the US has no legal definition of what constitutes a milkshake, leaving it up to the individual states to decide.

I also found this little snippet particularly interesting for this conversation:

As an ice cream drink, the 20th-century milkshake’s only serious contenders have been its legions of imitators. United States federal code defines ice cream down to the amount of air it may contain, but is silent on milkshakes, leaving their parameters to states. For restaurants with regional or national reach, the simplest way to sidestep dozens of states’ conflicting milkshake definitions within their territories is not to sell milkshakes. Many, instead, offer “shakes” or milkshake-adjacent frozen dessert drinks with branded names that suggest creamy coldness, but avoid the legal entanglements of calling them “milkshakes.”

This is why you end up with Blizzards and Frosties apparently!

https://imbibemagazine.com/american-milkshake-history/