To be honest, I'm not sure if I should contradict or confirm your comment because I don't come from a country where English is spoken and in my native language (Spanish) both terms mean the same thing. In any case, thank you for clarifying the situation, I will take it into account in the future.
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You're welcome.
I don't know Spanish but I can't imagine both terms mean the same thing. A Pay to Win game is exactly like you explained, you pay money for benefits in the game... maybe you purchase more powerful weapons or your buildings build faster.
A Play to Earn game is very different, you earn tokens for games that you win. You technically might not have to pay anything to be able to earn the tokens.