To equate two things is to treat them as the same, or as tightly linked — often in your mind, not in the real world.

To equate two thingsTo equate兩個東西 is to treat them as the same, or as tightly linked就是把它們當成一樣，或當成緊密相連的 — often in your mind通常是在你腦子裡這樣想 not in the real world不是現實世界真的如此

The usual shape is equate A with B: “Don’t equate money with happiness.” The speaker is often pushing back: those two things are not as close as someone thinks.

The usual shape is equate A with B常見的用法是equate A with B： 'Don't equate money with happiness.'「Don't equate money with happiness（不要把金錢和快樂畫上等號）」 The speaker is often pushing back說話者通常是在反駁： those two things are not as close as someone thinks這兩件事沒有某人想的那麼接近

It is common in essays and serious talk; in very simple speech you might say “that doesn’t mean the same as.” Though actually the word also lives in maths class, with a slightly different job: you equate two sides of an equation, you make them equal on paper. That use is colder and more exact.

It is common in essays and serious talk這個字常出現在文章和正式對話裡； in very simple speech you might say 'that doesn't mean the same as.'在非常口語的場合，你可能會說「that doesn't mean the same as（那跟……不是同一回事）」 Though actually不過事實上 the word also lives in maths class這個字在數學課裡也有一個用法 with a slightly different job稍微不同： you equate two sides of an equation你equate一個方程式的兩邊 you make them equal on paper讓它們在紙上相等。 That use is colder and more exact這個用法比較冷靜、也比較精確

The everyday use is almost never “these two things really are identical”; it is “someone is putting them in the same box.”

The everyday use is almost never 'these two things really are identical'日常用法幾乎不會是「這兩件事真的完全一樣」； it is 'someone is putting them in the same box.'而是「某人把它們放進了同一個框框裡」