It is not equivalent. Rare earths are, as you say, not actually that rare, but they are still a finite resource, and the CCP quite publicly discussed that it isn't a good idea to sell their domestic stockpile internationally while a significant amount of their economy runs on it. They raised prices to factor in that future availability might be more important than short-term profit.

The chip ban on the other hand is about R&D and labor, both things that do not diminish over time. Instead, the ban seeks to slow down Chinese advancement in areas relying on those chips, AI in particular. Both measures will lead to short-term issues, long-term lost growth, and mid-term new industries in the respective countries/markets.