You're making a huge logical leap. There is nothing equivalent about these claims other than that they are made in English.
> calling a language producing machine necessarily a thinking machine is an old old mistake.
Nobody claims that all language models think. The small markov chain language models of old clearly aren't thinking and produce a lot of gibberish. The difference is that, to the surprise of many people several years ago, but to the surprise of nobody who has been following along today, the corpus of all text produced by humans contains within it information about how the world works and also information about how to reason. Using that corpus to train a sufficiently large language model causes the language model to learn a world model and a reasoning model in order to produce text that matches the training data. The reasoning model can be used to perform longer chain thinking with test time compute techniques. People who think deeply for a living recognize thinking when they see it. https://scottaaronson.blog/?p=9979