When the Japanese sent embassies to China in the late 6th century and early 7th century (this would be the Sui Dynasty, followed by the Tang Dynasty), they discovered that the Chinese expected to see obeisance on the part of the visitors. While the Japanese were indeed overawed by this advanced society (they patterned their first planned capital city, Nara, after the Chinese capital’s layout, after all), they refused to show it outwardly.
So when the Chinese Emperor sends a letter to the Japanese government, the Japanese reply with identical words, to show that THEIR emperor is the same status as the Chinese Emperor.
In 607, the Japanese wrote “from the Emperor (Tenno: literally Heavenly Emperor) of the Rising Sun to the Emperor of the Setting Sun”.
This was the first time that the Japanese used the term Tenno to describe their ruler (which means that the Japanese “Emperor” was only an emperor vis-à-vis China and not because Japan was ever an “empire”) and the first time that the name “Japan” (which means “land of the rising sun” in Chinese) was used by the Japanese themselves (before that it was Yamato).
So, no, they were not of equal standing, but the Japanese pretended that they indeed WERE of equal standing.
An attitude that remains very strong indeed right up to the present day.