There is no boundless Buddha in Taoism.
The three infinity are: infinite vision, infinite life and infinite happiness. The origin of "three boundless" is very early. Later, because there was boundless Buddha in Buddhism, which was homophonic with Taoist infinite happiness, Taoism was changed to "boundless Buddha" in order to distinguish it. The boundless Buddha is Frodo. Infinite Buddha can't be used alone, only with others. Because there is no such thing as "boundless Buddha" in Taoism, it should be called "boundless Buddha".
The word of Taoism was originally "infinite longevity", which is a special word for blessing honesty, and it is different from the "Amitabha" of Buddhism; But the word "fu" in Taoism is pronounced the same as "Buddha" in southwest dialect. In order to avoid misinterpreting people's confusion about Tantric Buddhism's "infinite longevity Buddha" and "infinite longevity blessing", later Taoism in the whole country unified "Fu is the supreme Buddha" as the eternal holy name.
However, Taoist orthodoxy has the word "three boundless", which can also be regarded as "three boundless buddhas"; "Tianzun" does not represent any god in this word, but only promotes the word "boundless" to the highest level.
Taoism has such titles as "Infinite Respect for Man", "Infinite Respect for Life" and "Infinite Respect for Merit", all of which are complete titles of Buddha.
The Buddha with infinite longevity is a complete Buddha name.
Buddhists have the titles of "Amitabha Buddha" and "Infinite Life Buddha". "Amitabha Buddha" is a taboo of Buddha, and "Buddha" is a title. "Infinite life" means infinite life, and it is called "infinite life Buddha" in the name of Buddha. It can be said that this Buddha is the embodiment of life. It all makes sense. But the "boundless Buddha" is not. Taoism has such titles as "Infinite Respect for Man", "Infinite Respect for Life" and "Infinite Respect for Merit", all of which are complete titles of Buddha. But if we omit "measuring people", "longevity" and "merit" and only keep "boundless", that is to say, simplify the original title to "boundless Buddha", is that still the original intention? Obviously, if you look for meaning according to the text, "boundless Buddha" should be interpreted as "boundless Buddha" or "multi-Buddha". That's more like it? Is there such an abbreviation? In fact, it is not difficult for users to understand that "infinity" is the concept of quantity. How can it be called Buddha?