Acura has never been used in Japan. NSX and Integra are Honda models. Toyota introduced Lexus domestically in 2005. Their older Lexus models had Toyota equivalents, often as variants of the Toyota Crown which was their original luxury tier car.

That is accurate. Acura and Lexus were brands created for the US market. The original Integra was badged as Honda in Japan and Acura in the US, for example. A TLX or whatever is just a top trim Accord.

Lexus didn't enter the Japanese market as a brand until 2005, prior to that all Lexus models well sold under the Toyota moniker in the Japanese market. I'm not sure about Acura, but the GP's assertion is largely correct in its directionality.

I can confirm this is true for Acura. I owned an Acura Legend and the same car was sold in Japan (well, the right-hand drive version) as the Honda Legend. I had seen pictures of them online in the 90s, but happened to see a Honda Legend in person when I was in Tokyo some years later.

Acura is a brand made for North America. Just as in Japan, what you know as Acuras is sold in Europe as Hondas.