This is an important distinction. Most "rent control" laws are intended to be "rent stabilization" not outright price fixing. Their goal is to prevent insane swings in rent happening too quickly, which disrupts families and local economies (and even infrastructure development).
But the worst/most aggressively laws are always used as the examples, skewing the conversation to edge cases and ignoring the fact that these laws can and do take hundreds of different forms.
Price fixing isn't so bad either - if apt prices stay predictable, you can plane ahead financially without being forced to buy an apartment or house.